LMFDB - Embedded newform 425.2.m.d.151.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(26,425)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("425.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.m (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			151.5
Character	$\chi$	$=$	425.151
Dual form			425.2.m.d.76.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.917051 + 0.917051i) q^{2} +(0.703348 + 1.69803i) q^{3} -0.318036i q^{4} +(-0.912176 + 2.20219i) q^{6} +(3.23987 + 1.34200i) q^{7} +(2.12576 - 2.12576i) q^{8} +(-0.267297 + 0.267297i) q^{9} +O(q^{10})$	\(q+(0.917051 + 0.917051i) q^{2} +(0.703348 + 1.69803i) q^{3} -0.318036i q^{4} +(-0.912176 + 2.20219i) q^{6} +(3.23987 + 1.34200i) q^{7} +(2.12576 - 2.12576i) q^{8} +(-0.267297 + 0.267297i) q^{9} +(-1.46576 + 3.53865i) q^{11} +(0.540036 - 0.223690i) q^{12} -3.99064i q^{13} +(1.74044 + 4.20180i) q^{14} +3.26278 q^{16} +(-3.26350 + 2.51983i) q^{17} -0.490250 q^{18} +(-3.98810 - 3.98810i) q^{19} +6.44530i q^{21} +(-4.58929 + 1.90095i) q^{22} +(-0.960003 + 2.31765i) q^{23} +(5.10475 + 2.11446i) q^{24} +(3.65962 - 3.65962i) q^{26} +(4.45222 + 1.84417i) q^{27} +(0.426804 - 1.03040i) q^{28} +(-5.14221 + 2.12997i) q^{29} +(0.843138 + 2.03551i) q^{31} +(-1.25938 - 1.25938i) q^{32} -7.03968 q^{33} +(-5.30361 - 0.681982i) q^{34} +(0.0850102 + 0.0850102i) q^{36} +(-0.738686 - 1.78335i) q^{37} -7.31458i q^{38} +(6.77624 - 2.80681i) q^{39} +(0.730698 + 0.302665i) q^{41} +(-5.91066 + 5.91066i) q^{42} +(-0.704996 + 0.704996i) q^{43} +(1.12542 + 0.466164i) q^{44} +(-3.00578 + 1.24503i) q^{46} -9.47029i q^{47} +(2.29487 + 5.54031i) q^{48} +(3.74605 + 3.74605i) q^{49} +(-6.57414 - 3.76921i) q^{51} -1.26917 q^{52} +(-3.87552 - 3.87552i) q^{53} +(2.39171 + 5.77410i) q^{54} +(9.73994 - 4.03441i) q^{56} +(3.96690 - 9.57696i) q^{57} +(-6.66896 - 2.76238i) q^{58} +(2.12592 - 2.12592i) q^{59} +(-12.9789 - 5.37602i) q^{61} +(-1.09347 + 2.63987i) q^{62} +(-1.22472 + 0.507296i) q^{63} -8.83539i q^{64} +(-6.45574 - 6.45574i) q^{66} +15.9485 q^{67} +(0.801398 + 1.03791i) q^{68} -4.61067 q^{69} +(-2.09375 - 5.05477i) q^{71} +1.13642i q^{72} +(6.06784 - 2.51338i) q^{73} +(0.958006 - 2.31283i) q^{74} +(-1.26836 + 1.26836i) q^{76} +(-9.49772 + 9.49772i) q^{77} +(8.78814 + 3.64017i) q^{78} +(-4.54493 + 10.9724i) q^{79} +9.99115i q^{81} +(0.392528 + 0.947647i) q^{82} +(10.8309 + 10.8309i) q^{83} +2.04984 q^{84} -1.29303 q^{86} +(-7.23353 - 7.23353i) q^{87} +(4.40646 + 10.6381i) q^{88} -4.92175i q^{89} +(5.35543 - 12.9292i) q^{91} +(0.737098 + 0.305316i) q^{92} +(-2.86335 + 2.86335i) q^{93} +(8.68474 - 8.68474i) q^{94} +(1.25268 - 3.02425i) q^{96} +(13.1760 - 5.45769i) q^{97} +6.87064i q^{98} +(-0.554078 - 1.33766i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} + 12 q^{9}+O(q^{10}) $ 24 * q - 8 * q^6 + 12 * q^9	$ 24 q - 8 q^{6} + 12 q^{9} + 4 q^{11} + 12 q^{12} - 24 q^{14} - 24 q^{16} - 4 q^{17} + 40 q^{18} - 20 q^{19} - 16 q^{22} - 8 q^{23} + 16 q^{24} + 16 q^{26} + 12 q^{27} - 48 q^{28} + 4 q^{29} + 24 q^{31} + 60 q^{32} - 48 q^{33} + 16 q^{34} + 60 q^{36} + 12 q^{37} + 8 q^{39} - 20 q^{41} - 12 q^{42} - 32 q^{43} + 64 q^{44} - 40 q^{46} + 40 q^{48} + 24 q^{49} + 16 q^{51} + 48 q^{52} + 12 q^{53} - 20 q^{54} - 32 q^{56} - 68 q^{57} + 16 q^{58} - 16 q^{59} - 64 q^{61} - 100 q^{62} + 44 q^{63} - 72 q^{66} - 40 q^{67} - 20 q^{68} - 48 q^{69} - 24 q^{71} + 32 q^{74} + 52 q^{76} - 24 q^{77} + 16 q^{78} - 48 q^{79} - 100 q^{82} - 12 q^{83} - 40 q^{84} - 16 q^{86} - 24 q^{87} - 4 q^{88} + 24 q^{91} + 88 q^{92} + 32 q^{93} - 40 q^{94} + 132 q^{96} + 88 q^{97} - 80 q^{99}+O(q^{100}) $ 24 * q - 8 * q^6 + 12 * q^9 + 4 * q^11 + 12 * q^12 - 24 * q^14 - 24 * q^16 - 4 * q^17 + 40 * q^18 - 20 * q^19 - 16 * q^22 - 8 * q^23 + 16 * q^24 + 16 * q^26 + 12 * q^27 - 48 * q^28 + 4 * q^29 + 24 * q^31 + 60 * q^32 - 48 * q^33 + 16 * q^34 + 60 * q^36 + 12 * q^37 + 8 * q^39 - 20 * q^41 - 12 * q^42 - 32 * q^43 + 64 * q^44 - 40 * q^46 + 40 * q^48 + 24 * q^49 + 16 * q^51 + 48 * q^52 + 12 * q^53 - 20 * q^54 - 32 * q^56 - 68 * q^57 + 16 * q^58 - 16 * q^59 - 64 * q^61 - 100 * q^62 + 44 * q^63 - 72 * q^66 - 40 * q^67 - 20 * q^68 - 48 * q^69 - 24 * q^71 + 32 * q^74 + 52 * q^76 - 24 * q^77 + 16 * q^78 - 48 * q^79 - 100 * q^82 - 12 * q^83 - 40 * q^84 - 16 * q^86 - 24 * q^87 - 4 * q^88 + 24 * q^91 + 88 * q^92 + 32 * q^93 - 40 * q^94 + 132 * q^96 + 88 * q^97 - 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.917051	+	0.917051i	0.648453	+	0.648453i	0.952619	−	0.304166i	$-0.0983778\pi$
$2$	0.917051	+	0.917051i	0.648453	+	0.648453i	−0.304166	+	0.952619i	$0.598378\pi$
$3$	0.703348	+	1.69803i	0.406078	+	0.980360i	0.986159	+	0.165801i	$0.0530209\pi$
$3$	0.703348	+	1.69803i	0.406078	+	0.980360i	−0.580081	+	0.814559i	$0.696979\pi$
$4$		−	0.318036i		−	0.159018i
$5$		0			0
$5$		0			0
$6$	−0.912176	+	2.20219i	−0.372394	+	0.899040i
$7$	3.23987	+	1.34200i	1.22456	+	0.507228i	0.898855	−	0.438245i	$-0.144400\pi$
$7$	3.23987	+	1.34200i	1.22456	+	0.507228i	0.325700	+	0.945473i	$0.394400\pi$
$8$	2.12576	−	2.12576i	0.751568	−	0.751568i
$9$	−0.267297	+	0.267297i	−0.0890990	+	0.0890990i
$10$		0			0
$11$	−1.46576	+	3.53865i	−0.441942	+	1.06694i	0.533325	+	0.845911i	$0.320942\pi$
$11$	−1.46576	+	3.53865i	−0.441942	+	1.06694i	−0.975267	+	0.221032i	$0.929058\pi$
$12$	0.540036	−	0.223690i	0.155895	−	0.0645738i
$13$		−	3.99064i		−	1.10680i	−0.832914	−	0.553402i	$-0.813329\pi$
$13$		−	3.99064i		−	1.10680i	0.832914	−	0.553402i	$-0.186671\pi$
$14$	1.74044	+	4.20180i	0.465153	+	1.12298i
$15$		0			0
$16$	3.26278			0.815695
$17$	−3.26350	+	2.51983i	−0.791515	+	0.611149i
$17$	−3.26350	+	2.51983i	−0.791515	+	0.611149i
$18$	−0.490250			−0.115553
$19$	−3.98810	−	3.98810i	−0.914933	−	0.914933i	0.0817217	−	0.996655i	$-0.473958\pi$
$19$	−3.98810	−	3.98810i	−0.914933	−	0.914933i	−0.996655	+	0.0817217i	$0.973958\pi$
$20$		0			0
$21$			6.44530i			1.40648i
$22$	−4.58929	+	1.90095i	−0.978440	+	0.405283i
$23$	−0.960003	+	2.31765i	−0.200175	+	0.483264i	−0.991809	−	0.127731i	$-0.959231\pi$
$23$	−0.960003	+	2.31765i	−0.200175	+	0.483264i	0.791634	+	0.610995i	$0.209231\pi$
$24$	5.10475	+	2.11446i	1.04200	+	0.431612i
$25$		0			0
$26$	3.65962	−	3.65962i	0.717710	−	0.717710i
$27$	4.45222	+	1.84417i	0.856830	+	0.354910i
$28$	0.426804	−	1.03040i	0.0806584	−	0.194727i
$29$	−5.14221	+	2.12997i	−0.954885	+	0.395526i	−0.805065	−	0.593187i	$-0.797870\pi$
$29$	−5.14221	+	2.12997i	−0.954885	+	0.395526i	−0.149820	+	0.988713i	$0.547870\pi$
$30$		0			0
$31$	0.843138	+	2.03551i	0.151432	+	0.365589i	0.981332	−	0.192324i	$-0.0616023\pi$
$31$	0.843138	+	2.03551i	0.151432	+	0.365589i	−0.829900	+	0.557913i	$0.811602\pi$
$32$	−1.25938	−	1.25938i	−0.222629	−	0.222629i
$33$	−7.03968			−1.22545
$34$	−5.30361	−	0.681982i	−0.909562	−	0.116959i
$35$		0			0
$36$	0.0850102	+	0.0850102i	0.0141684	+	0.0141684i
$37$	−0.738686	−	1.78335i	−0.121439	−	0.293180i	0.851456	−	0.524426i	$-0.175720\pi$
$37$	−0.738686	−	1.78335i	−0.121439	−	0.293180i	−0.972895	+	0.231245i	$0.925720\pi$
$38$		−	7.31458i		−	1.18658i
$39$	6.77624	−	2.80681i	1.08507	−	0.449449i
$40$		0			0
$41$	0.730698	+	0.302665i	0.114116	+	0.0472684i	0.439011	−	0.898482i	$-0.355329\pi$
$41$	0.730698	+	0.302665i	0.114116	+	0.0472684i	−0.324895	+	0.945750i	$0.605329\pi$
$42$	−5.91066	+	5.91066i	−0.912035	+	0.912035i
$43$	−0.704996	+	0.704996i	−0.107511	+	0.107511i	−0.758816	−	0.651305i	$-0.774222\pi$
$43$	−0.704996	+	0.704996i	−0.107511	+	0.107511i	0.651305	+	0.758816i	$0.274222\pi$
$44$	1.12542	+	0.466164i	0.169663	+	0.0702768i
$45$		0			0
$46$	−3.00578	+	1.24503i	−0.443178	+	0.183570i
$47$		−	9.47029i		−	1.38138i	−0.723149	−	0.690692i	$-0.757306\pi$
$47$		−	9.47029i		−	1.38138i	0.723149	−	0.690692i	$-0.242694\pi$
$48$	2.29487	+	5.54031i	0.331236	+	0.799675i
$49$	3.74605	+	3.74605i	0.535150	+	0.535150i
$50$		0			0
$51$	−6.57414	−	3.76921i	−0.920563	−	0.527796i
$52$	−1.26917			−0.176002
$53$	−3.87552	−	3.87552i	−0.532344	−	0.532344i	0.388925	−	0.921269i	$-0.372846\pi$
$53$	−3.87552	−	3.87552i	−0.532344	−	0.532344i	−0.921269	+	0.388925i	$0.872846\pi$
$54$	2.39171	+	5.77410i	0.325471	+	0.785756i
$55$		0			0
$56$	9.73994	−	4.03441i	1.30155	−	0.539121i
$57$	3.96690	−	9.57696i	0.525429	−	1.26850i
$58$	−6.66896	−	2.76238i	−0.875678	−	0.362718i
$59$	2.12592	−	2.12592i	0.276771	−	0.276771i	−0.555048	−	0.831819i	$-0.687300\pi$
$59$	2.12592	−	2.12592i	0.276771	−	0.276771i	0.831819	+	0.555048i	$0.187300\pi$
$60$		0			0
$61$	−12.9789	−	5.37602i	−1.66177	−	0.688329i	−0.663563	−	0.748120i	$-0.730957\pi$
$61$	−12.9789	−	5.37602i	−1.66177	−	0.688329i	−0.998211	+	0.0597912i	$0.980957\pi$
$62$	−1.09347	+	2.63987i	−0.138871	+	0.335264i
$63$	−1.22472	+	0.507296i	−0.154300	+	0.0639132i
$64$		−	8.83539i		−	1.10442i
$65$		0			0
$66$	−6.45574	−	6.45574i	−0.794647	−	0.794647i
$67$	15.9485			1.94842			0.974210	−	0.225645i	$-0.0724488\pi$
$67$	15.9485			1.94842			0.974210	+	0.225645i	$0.0724488\pi$
$68$	0.801398	+	1.03791i	0.0971838	+	0.125865i
$69$	−4.61067			−0.555059
$70$		0			0
$71$	−2.09375	−	5.05477i	−0.248483	−	0.599890i	0.749593	−	0.661899i	$-0.230249\pi$
$71$	−2.09375	−	5.05477i	−0.248483	−	0.599890i	−0.998076	+	0.0620087i	$0.980249\pi$
$72$			1.13642i			0.133928i
$73$	6.06784	−	2.51338i	0.710187	−	0.294169i	0.00180494	−	0.999998i	$-0.499425\pi$
$73$	6.06784	−	2.51338i	0.710187	−	0.294169i	0.708382	+	0.705829i	$0.249425\pi$
$74$	0.958006	−	2.31283i	0.111366	−	0.268861i
$75$		0			0
$76$	−1.26836	+	1.26836i	−0.145491	+	0.145491i
$77$	−9.49772	+	9.49772i	−1.08237	+	1.08237i
$78$	8.78814	+	3.64017i	0.995061	+	0.412168i
$79$	−4.54493	+	10.9724i	−0.511344	+	1.23449i	0.431757	+	0.901990i	$0.357894\pi$
$79$	−4.54493	+	10.9724i	−0.511344	+	1.23449i	−0.943102	+	0.332505i	$0.892106\pi$
$80$		0			0
$81$			9.99115i			1.11013i
$82$	0.392528	+	0.947647i	0.0433475	+	0.104650i
$83$	10.8309	+	10.8309i	1.18885	+	1.18885i	0.977386	+	0.211461i	$0.0678222\pi$
$83$	10.8309	+	10.8309i	1.18885	+	1.18885i	0.211461	+	0.977386i	$0.432178\pi$
$84$	2.04984			0.223656
$85$		0			0
$86$	−1.29303			−0.139431
$87$	−7.23353	−	7.23353i	−0.775516	−	0.775516i
$88$	4.40646	+	10.6381i	0.469731	+	1.13403i
$89$		−	4.92175i		−	0.521705i	−0.965379	−	0.260852i	$-0.915996\pi$
$89$		−	4.92175i		−	0.521705i	0.965379	−	0.260852i	$-0.0840036\pi$
$90$		0			0
$91$	5.35543	−	12.9292i	0.561402	−	1.35534i
$92$	0.737098	+	0.305316i	0.0768477	+	0.0318314i
$93$	−2.86335	+	2.86335i	−0.296916	+	0.296916i
$94$	8.68474	−	8.68474i	0.895762	−	0.895762i
$95$		0			0
$96$	1.25268	−	3.02425i	0.127852	−	0.308661i
$97$	13.1760	−	5.45769i	1.33782	−	0.554145i	0.404947	−	0.914340i	$-0.367290\pi$
$97$	13.1760	−	5.45769i	1.33782	−	0.554145i	0.932877	+	0.360195i	$0.117290\pi$
$98$			6.87064i			0.694039i
$99$	−0.554078	−	1.33766i	−0.0556869	−	0.134440i
$100$		0			0
$101$	16.9268			1.68428			0.842138	−	0.539263i	$-0.181297\pi$
$101$	16.9268			1.68428			0.842138	+	0.539263i	$0.181297\pi$
$102$	−2.57226	−	9.48538i	−0.254691	−	0.939192i
$103$	−3.26693			−0.321900			−0.160950	−	0.986963i	$-0.551456\pi$
$103$	−3.26693			−0.321900			−0.160950	+	0.986963i	$0.551456\pi$
$104$	−8.48313	−	8.48313i	−0.831839	−	0.831839i
$105$		0			0
$106$		−	7.10810i		−	0.690399i
$107$	−4.39224	+	1.81933i	−0.424614	+	0.175881i	−0.584749	−	0.811214i	$-0.698807\pi$
$107$	−4.39224	+	1.81933i	−0.424614	+	0.175881i	0.160135	+	0.987095i	$0.448807\pi$
$108$	0.586512	−	1.41597i	0.0564372	−	0.136251i
$109$	−15.2446	−	6.31451i	−1.46017	−	0.604820i	−0.495573	−	0.868566i	$-0.665042\pi$
$109$	−15.2446	−	6.31451i	−1.46017	−	0.604820i	−0.964592	+	0.263746i	$0.915042\pi$
$110$		0			0
$111$	2.50863	−	2.50863i	0.238108	−	0.238108i
$112$	10.5710	+	4.37864i	0.998864	+	0.413743i
$113$	−4.26597	+	10.2990i	−0.401309	+	0.968845i	0.586040	+	0.810282i	$0.300686\pi$
$113$	−4.26597	+	10.2990i	−0.401309	+	0.968845i	−0.987349	+	0.158563i	$0.949314\pi$
$114$	12.4204	−	5.14470i	1.16328	−	0.481845i
$115$		0			0
$116$	0.677409	+	1.63541i	0.0628959	+	0.151844i
$117$	1.06669	+	1.06669i	0.0986152	+	0.0986152i
$118$	3.89915			0.358946
$119$	−13.9549	+	3.78432i	−1.27925	+	0.346908i
$120$		0			0
$121$	−2.59541	−	2.59541i	−0.235947	−	0.235947i
$122$	−6.97219	−	16.8324i	−0.631233	−	1.52393i
$123$			1.45363i			0.131069i
$124$	0.647367	−	0.268148i	0.0581353	−	0.0240804i
$125$		0			0
$126$	−1.58835	−	0.657914i	−0.141501	−	0.0586117i
$127$	0.759855	−	0.759855i	0.0674262	−	0.0674262i	−0.672590	−	0.740016i	$-0.734818\pi$
$127$	0.759855	−	0.759855i	0.0674262	−	0.0674262i	0.740016	+	0.672590i	$0.234818\pi$
$128$	5.58374	−	5.58374i	0.493538	−	0.493538i
$129$	−1.69296	−	0.701248i	−0.149057	−	0.0617415i
$130$		0			0
$131$	−9.50053	+	3.93525i	−0.830065	+	0.343824i	−0.756928	−	0.653498i	$-0.773301\pi$
$131$	−9.50053	+	3.93525i	−0.830065	+	0.343824i	−0.0731364	+	0.997322i	$0.523301\pi$
$132$			2.23887i			0.194869i
$133$	−7.56891	−	18.2730i	−0.656308	−	1.58447i
$134$	14.6256	+	14.6256i	1.26346	+	1.26346i
$135$		0			0
$136$	−1.58086	+	12.2940i	−0.135558	+	1.05420i
$137$	−14.4834			−1.23740			−0.618700	−	0.785627i	$-0.712340\pi$
$137$	−14.4834			−1.23740			−0.618700	+	0.785627i	$0.712340\pi$
$138$	−4.22822	−	4.22822i	−0.359930	−	0.359930i
$139$	−2.25636	−	5.44734i	−0.191382	−	0.462037i	0.798839	−	0.601545i	$-0.205448\pi$
$139$	−2.25636	−	5.44734i	−0.191382	−	0.462037i	−0.990221	+	0.139508i	$0.955448\pi$
$140$		0			0
$141$	16.0809	−	6.66092i	1.35425	−	0.560950i
$142$	2.71540	−	6.55555i	0.227871	−	0.550130i
$143$	14.1215	+	5.84930i	1.18090	+	0.489143i
$144$	−0.872132	+	0.872132i	−0.0726776	+	0.0726776i
$145$		0			0
$146$	7.86941	+	3.25962i	0.651277	+	0.269768i
$147$	−3.72614	+	8.99570i	−0.307327	+	0.741952i
$148$	−0.567169	+	0.234929i	−0.0466210	+	0.0193110i
$149$			14.8500i			1.21656i	0.793723	+	0.608279i	$0.208140\pi$
$149$			14.8500i			1.21656i	−0.793723	+	0.608279i	$0.791860\pi$
$150$		0			0
$151$	−11.2249	−	11.2249i	−0.913467	−	0.913467i	0.0830762	−	0.996543i	$-0.473526\pi$
$151$	−11.2249	−	11.2249i	−0.913467	−	0.913467i	−0.996543	+	0.0830762i	$0.973526\pi$
$152$	−16.9555			−1.37527
$153$	0.198781	−	1.54587i	0.0160705	−	0.124976i
$154$	−17.4198			−1.40373
$155$		0			0
$156$	−0.892667	−	2.15509i	−0.0714706	−	0.172545i
$157$			14.0842i			1.12404i	0.827122	+	0.562022i	$0.189976\pi$
$157$			14.0842i			1.12404i	−0.827122	+	0.562022i	$0.810024\pi$
$158$	−14.2302	+	5.89434i	−1.13209	+	0.468929i
$159$	3.85492	−	9.30660i	0.305715	−	0.738062i
$160$		0			0
$161$	−6.22057	+	6.22057i	−0.490250	+	0.490250i
$162$	−9.16239	+	9.16239i	−0.719865	+	0.719865i
$163$	−13.9123	−	5.76267i	−1.08970	−	0.451367i	−0.235795	−	0.971803i	$-0.575770\pi$
$163$	−13.9123	−	5.76267i	−1.08970	−	0.451367i	−0.853901	+	0.520436i	$0.825770\pi$
$164$	0.0962585	−	0.232389i	0.00751653	−	0.0181465i
$165$		0			0
$166$			19.8650i			1.54182i
$167$	4.20048	+	10.1409i	0.325043	+	0.784723i	0.998946	+	0.0459030i	$0.0146165\pi$
$167$	4.20048	+	10.1409i	0.325043	+	0.784723i	−0.673903	+	0.738820i	$0.735383\pi$
$168$	13.7011	+	13.7011i	1.05707	+	1.05707i
$169$	−2.92520			−0.225015
$170$		0			0
$171$	2.13202			0.163039
$172$	0.224214	+	0.224214i	0.0170962	+	0.0170962i
$173$	−0.887514	−	2.14265i	−0.0674764	−	0.162903i	0.886544	−	0.462645i	$-0.153099\pi$
$173$	−0.887514	−	2.14265i	−0.0674764	−	0.162903i	−0.954020	+	0.299742i	$0.903099\pi$
$174$		−	13.2670i		−	1.00577i
$175$		0			0
$176$	−4.78244	+	11.5458i	−0.360490	+	0.870300i
$177$	5.10514	+	2.11462i	0.383726	+	0.158944i
$178$	4.51350	−	4.51350i	0.338301	−	0.338301i
$179$	−11.8583	+	11.8583i	−0.886330	+	0.886330i	−0.994168	−	0.107839i	$-0.965607\pi$
$179$	−11.8583	+	11.8583i	−0.886330	+	0.886330i	0.107839	+	0.994168i	$0.465607\pi$
$180$		0			0
$181$	2.39181	−	5.77433i	0.177782	−	0.429203i	−0.809719	−	0.586818i	$-0.800380\pi$
$181$	2.39181	−	5.77433i	0.177782	−	0.429203i	0.987501	+	0.157615i	$0.0503805\pi$
$182$	16.7679	−	6.94549i	1.24292	−	0.514834i
$183$		−	25.8198i		−	1.90865i
$184$	2.88603	+	6.96750i	0.212761	+	0.513651i
$185$		0			0
$186$	−5.25168			−0.385072
$187$	−4.13330	−	15.2418i	−0.302257	−	1.11459i
$188$	−3.01190			−0.219665
$189$	11.9497	+	11.9497i	0.869215	+	0.869215i
$190$		0			0
$191$		−	8.01061i		−	0.579627i	−0.957083	−	0.289814i	$-0.906407\pi$
$191$		−	8.01061i		−	0.579627i	0.957083	−	0.289814i	$-0.0935934\pi$
$192$	15.0028	−	6.21436i	1.08273	−	0.448482i
$193$	−5.58990	+	13.4952i	−0.402370	+	0.971406i	0.584720	+	0.811235i	$0.301204\pi$
$193$	−5.58990	+	13.4952i	−0.402370	+	0.971406i	−0.987089	+	0.160171i	$0.948796\pi$
$194$	17.0881	+	7.07811i	1.22685	+	0.508179i
$195$		0			0
$196$	1.19138	−	1.19138i	0.0850986	−	0.0850986i
$197$	8.68984	+	3.59945i	0.619125	+	0.256450i	0.670125	−	0.742249i	$-0.266241\pi$
$197$	8.68984	+	3.59945i	0.619125	+	0.256450i	−0.0509993	+	0.998699i	$0.516241\pi$
$198$	0.718587	−	1.73482i	0.0510677	−	0.123288i
$199$	17.8952	−	7.41242i	1.26855	−	0.525452i	0.356030	−	0.934475i	$-0.384130\pi$
$199$	17.8952	−	7.41242i	1.26855	−	0.525452i	0.912524	+	0.409022i	$0.134130\pi$
$200$		0			0
$201$	11.2174	+	27.0811i	0.791211	+	1.91015i
$202$	15.5227	+	15.5227i	1.09217	+	1.09217i
$203$	−19.5185			−1.36993
$204$	−1.19875	+	2.09081i	−0.0839291	+	0.146386i
$205$		0			0
$206$	−2.99594	−	2.99594i	−0.208737	−	0.208737i
$207$	−0.362896	−	0.876108i	−0.0252230	−	0.0608937i
$208$		−	13.0206i		−	0.902815i
$209$	19.9581	−	8.26691i	1.38053	−	0.571834i
$210$		0			0
$211$	−17.0199	−	7.04985i	−1.17169	−	0.485332i	−0.289942	−	0.957044i	$-0.593636\pi$
$211$	−17.0199	−	7.04985i	−1.17169	−	0.485332i	−0.881753	+	0.471712i	$0.843636\pi$
$212$	−1.23256	+	1.23256i	−0.0846523	+	0.0846523i
$213$	7.11052	−	7.11052i	0.487205	−	0.487205i
$214$	−5.69632	−	2.35949i	−0.389393	−	0.161292i
$215$		0			0
$216$	13.3846	−	5.54408i	0.910706	−	0.377227i
$217$			7.72629i			0.524495i
$218$	−8.18932	−	19.7708i	−0.554651	−	1.33905i
$219$	8.53561	+	8.53561i	0.576783	+	0.576783i
$220$		0			0
$221$	10.0557	+	13.0235i	0.676422	+	0.876053i
$222$	4.60108			0.308804
$223$	9.31157	+	9.31157i	0.623549	+	0.623549i	0.946437	−	0.322888i	$-0.104654\pi$
$223$	9.31157	+	9.31157i	0.623549	+	0.623549i	−0.322888	+	0.946437i	$0.604654\pi$
$224$	−2.39014	−	5.77031i	−0.159698	−	0.385545i
$225$		0			0
$226$	−13.3568	+	5.53256i	−0.888480	+	0.368020i
$227$	6.96624	−	16.8180i	0.462366	−	1.11625i	−0.505058	−	0.863086i	$-0.668529\pi$
$227$	6.96624	−	16.8180i	0.462366	−	1.11625i	0.967423	−	0.253164i	$-0.0814712\pi$
$228$	−3.04582	−	1.26162i	−0.201714	−	0.0835528i
$229$	−9.84208	+	9.84208i	−0.650383	+	0.650383i	−0.953085	−	0.302702i	$-0.902111\pi$
$229$	−9.84208	+	9.84208i	−0.650383	+	0.650383i	0.302702	+	0.953085i	$0.402111\pi$
$230$		0			0
$231$	−22.8076	−	9.44723i	−1.50063	−	0.621582i
$232$	−6.40329	+	15.4589i	−0.420396	+	1.01493i
$233$	8.75738	−	3.62743i	0.573715	−	0.237641i	−0.0769120	−	0.997038i	$-0.524506\pi$
$233$	8.75738	−	3.62743i	0.573715	−	0.237641i	0.650627	+	0.759397i	$0.274506\pi$
$234$			1.95641i			0.127895i
$235$		0			0
$236$	−0.676119	−	0.676119i	−0.0440116	−	0.0440116i
$237$	−21.8282			−1.41789
$238$	−16.2678	−	9.32697i	−1.05448	−	0.604578i
$239$	18.3775			1.18874			0.594371	−	0.804191i	$-0.297401\pi$
$239$	18.3775			1.18874			0.594371	+	0.804191i	$0.297401\pi$
$240$		0			0
$241$	7.66503	+	18.5050i	0.493748	+	1.19201i	0.952799	+	0.303603i	$0.0981895\pi$
$241$	7.66503	+	18.5050i	0.493748	+	1.19201i	−0.459051	+	0.888410i	$0.651811\pi$
$242$		−	4.76025i		−	0.306001i
$243$	−3.60865	+	1.49475i	−0.231495	+	0.0958884i
$244$	−1.70977	+	4.12775i	−0.109457	+	0.264252i
$245$		0			0
$246$	−1.33305	+	1.33305i	−0.0849922	+	0.0849922i
$247$	−15.9151	+	15.9151i	−1.01265	+	1.01265i
$248$	6.11931	+	2.53470i	0.388577	+	0.160954i
$249$	−10.7733	+	26.0092i	−0.682733	+	1.64826i
$250$		0			0
$251$			4.89225i			0.308796i	0.988009	+	0.154398i	$0.0493438\pi$
$251$			4.89225i			0.308796i	−0.988009	+	0.154398i	$0.950656\pi$
$252$	0.161338	+	0.389505i	0.0101634	+	0.0245365i
$253$	−6.79423	−	6.79423i	−0.427149	−	0.427149i
$254$	1.39365			0.0874455
$255$		0			0
$256$	−7.42963			−0.464352
$257$	12.3362	+	12.3362i	0.769509	+	0.769509i	0.978020	−	0.208511i	$-0.0668617\pi$
$257$	12.3362	+	12.3362i	0.769509	+	0.769509i	−0.208511	+	0.978020i	$0.566862\pi$
$258$	−0.909453	−	2.19561i	−0.0566201	−	0.136693i
$259$		−	6.76913i		−	0.420613i
$260$		0			0
$261$	0.805163	−	1.94383i	0.0498383	−	0.120320i
$262$	−12.3213	−	5.10364i	−0.761211	−	0.315304i
$263$	3.38705	−	3.38705i	0.208854	−	0.208854i	−0.594926	−	0.803780i	$-0.702819\pi$
$263$	3.38705	−	3.38705i	0.208854	−	0.208854i	0.803780	+	0.594926i	$0.202819\pi$
$264$	−14.9646	+	14.9646i	−0.921010	+	0.921010i
$265$		0			0
$266$	9.81616	−	23.6983i	0.601867	−	1.45304i
$267$	8.35730	−	3.46171i	0.511458	−	0.211853i
$268$		−	5.07220i		−	0.309834i
$269$	−4.70460	−	11.3579i	−0.286844	−	0.692504i	0.713119	−	0.701043i	$-0.247282\pi$
$269$	−4.70460	−	11.3579i	−0.286844	−	0.692504i	−0.999964	+	0.00853923i	$0.997282\pi$
$270$		0			0
$271$	30.4084			1.84718			0.923591	−	0.383380i	$-0.125240\pi$
$271$	30.4084			1.84718			0.923591	+	0.383380i	$0.125240\pi$
$272$	−10.6481	+	8.22166i	−0.645635	+	0.498511i
$273$	25.7209			1.55670
$274$	−13.2820	−	13.2820i	−0.802395	−	0.802395i
$275$		0			0
$276$			1.46636i			0.0882645i
$277$	4.97137	−	2.05921i	0.298700	−	0.123726i	−0.228300	−	0.973591i	$-0.573317\pi$
$277$	4.97137	−	2.05921i	0.298700	−	0.123726i	0.527000	+	0.849865i	$0.323317\pi$
$278$	2.92629	−	7.06469i	0.175507	−	0.423712i
$279$	−0.769455	−	0.318719i	−0.0460661	−	0.0190812i
$280$		0			0
$281$	−19.2856	+	19.2856i	−1.15048	+	1.15048i	−0.164027	+	0.986456i	$0.552448\pi$
$281$	−19.2856	+	19.2856i	−1.15048	+	1.15048i	−0.986456	+	0.164027i	$0.947552\pi$
$282$	20.8554	+	8.63858i	1.24192	+	0.514420i
$283$	−9.59747	+	23.1703i	−0.570511	+	1.37733i	0.330611	+	0.943767i	$0.392745\pi$
$283$	−9.59747	+	23.1703i	−0.570511	+	1.37733i	−0.901121	+	0.433567i	$0.857255\pi$
$284$	−1.60760	+	0.665889i	−0.0953935	+	0.0395133i
$285$		0			0
$286$	7.58599	+	18.3142i	0.448569	+	1.08294i
$287$	1.96119	+	1.96119i	0.115765	+	0.115765i
$288$	0.673256			0.0396720
$289$	4.30089	−	16.4470i	0.252993	−	0.967468i
$290$		0			0
$291$	18.5347	+	18.5347i	1.08652	+	1.08652i
$292$	−0.799346	−	1.92979i	−0.0467782	−	0.112933i
$293$			4.22198i			0.246651i	0.992366	+	0.123325i	$0.0393559\pi$
$293$			4.22198i			0.246651i	−0.992366	+	0.123325i	$0.960644\pi$
$294$	−11.6666	+	4.83245i	−0.680408	+	0.281834i
$295$		0			0
$296$	−5.36123	−	2.22069i	−0.311615	−	0.129075i
$297$	−13.0517	+	13.0517i	−0.757338	+	0.757338i
$298$	−13.6182	+	13.6182i	−0.788881	+	0.788881i
$299$	9.24892	+	3.83103i	0.534879	+	0.221554i
$300$		0			0
$301$	−3.23020	+	1.33799i	−0.186185	+	0.0771205i
$302$		−	20.5875i		−	1.18468i
$303$	11.9054	+	28.7422i	0.683948	+	1.65120i
$304$	−13.0123	−	13.0123i	−0.746307	−	0.746307i
$305$		0			0
$306$	1.59993	−	1.23535i	0.0914620	−	0.0706201i
$307$	−10.9167			−0.623050			−0.311525	−	0.950238i	$-0.600840\pi$
$307$	−10.9167			−0.623050			−0.311525	+	0.950238i	$0.600840\pi$
$308$	3.02062	+	3.02062i	0.172116	+	0.172116i
$309$	−2.29779	−	5.54735i	−0.130717	−	0.315578i
$310$		0			0
$311$	13.2842	−	5.50248i	0.753275	−	0.312017i	0.0271980	−	0.999630i	$-0.491342\pi$
$311$	13.2842	−	5.50248i	0.753275	−	0.312017i	0.726077	+	0.687613i	$0.241342\pi$
$312$	8.43804	−	20.3712i	0.477710	−	1.15329i
$313$	0.686474	+	0.284347i	0.0388018	+	0.0160722i	0.402000	−	0.915640i	$-0.368315\pi$
$313$	0.686474	+	0.284347i	0.0388018	+	0.0160722i	−0.363198	+	0.931712i	$0.618315\pi$
$314$	−12.9160	+	12.9160i	−0.728889	+	0.728889i
$315$		0			0
$316$	3.48963	+	1.44545i	0.196307	+	0.0813130i
$317$	−8.11763	+	19.5977i	−0.455931	+	1.10072i	0.514099	+	0.857731i	$0.328127\pi$
$317$	−8.11763	+	19.5977i	−0.455931	+	1.10072i	−0.970030	+	0.242985i	$0.921873\pi$
$318$	12.0698	−	4.99947i	0.676840	−	0.280356i
$319$		−	21.3185i		−	1.19361i
$320$		0			0
$321$	−6.17855	−	6.17855i	−0.344853	−	0.344853i
$322$	−11.4092			−0.635807
$323$	23.0645	+	2.96583i	1.28334	+	0.165023i
$324$	3.17755			0.176530
$325$		0			0
$326$	−7.47363	−	18.0429i	−0.413926	−	0.999307i
$327$		−	30.3271i		−	1.67709i
$328$	2.19668	−	0.909894i	0.121291	−	0.0502405i
$329$	12.7091	−	30.6825i	0.700676	−	1.69158i
$330$		0			0
$331$	18.9788	−	18.9788i	1.04317	−	1.04317i	0.0441412	−	0.999025i	$-0.485945\pi$
$331$	18.9788	−	18.9788i	1.04317	−	1.04317i	0.999025	−	0.0441412i	$-0.0140551\pi$
$332$	3.44462	−	3.44462i	0.189048	−	0.189048i
$333$	0.674132	+	0.279235i	0.0369422	+	0.0153020i
$334$	−5.44762	+	13.1517i	−0.298081	+	0.719631i
$335$		0			0
$336$			21.0296i			1.14726i
$337$	1.70719	+	4.12153i	0.0929968	+	0.224514i	0.963533	−	0.267591i	$-0.0862276\pi$
$337$	1.70719	+	4.12153i	0.0929968	+	0.224514i	−0.870536	+	0.492105i	$0.836228\pi$
$338$	−2.68256	−	2.68256i	−0.145912	−	0.145912i
$339$	−20.4884			−1.11278
$340$		0			0
$341$	−8.43880			−0.456987
$342$	1.95517	+	1.95517i	0.105723	+	0.105723i
$343$	−2.28446	−	5.51518i	−0.123349	−	0.297792i
$344$			2.99730i			0.161603i
$345$		0			0
$346$	1.15102	−	2.77881i	0.0618793	−	0.149390i
$347$	4.31193	+	1.78606i	0.231476	+	0.0958807i	0.495407	−	0.868661i	$-0.335019\pi$
$347$	4.31193	+	1.78606i	0.231476	+	0.0958807i	−0.263930	+	0.964542i	$0.585019\pi$
$348$	−2.30053	+	2.30053i	−0.123321	+	0.123321i
$349$	−1.58298	+	1.58298i	−0.0847348	+	0.0847348i	−0.748204	−	0.663469i	$-0.769083\pi$
$349$	−1.58298	+	1.58298i	−0.0847348	+	0.0847348i	0.663469	+	0.748204i	$0.269083\pi$
$350$		0			0
$351$	7.35941	−	17.7672i	0.392816	−	0.948343i
$352$	6.30244	−	2.61056i	0.335921	−	0.139143i
$353$			0.575628i			0.0306376i	0.999883	+	0.0153188i	$0.00487632\pi$
$353$			0.575628i			0.0306376i	−0.999883	+	0.0153188i	$0.995124\pi$
$354$	2.74246	+	6.62088i	0.145760	+	0.351896i
$355$		0			0
$356$	−1.56530			−0.0829605
$357$	−16.2411	−	21.0342i	−0.859569	−	1.11325i
$358$	−21.7493			−1.14949
$359$	7.66031	+	7.66031i	0.404296	+	0.404296i	0.879744	−	0.475448i	$-0.157714\pi$
$359$	7.66031	+	7.66031i	0.404296	+	0.404296i	−0.475448	+	0.879744i	$0.657714\pi$
$360$		0			0
$361$			12.8099i			0.674207i
$362$	7.48877	−	3.10195i	0.393601	−	0.163035i
$363$	2.58162	−	6.23258i	0.135500	−	0.327126i
$364$	−4.11194	−	1.70322i	−0.215524	−	0.0892730i
$365$		0			0
$366$	23.6780	−	23.6780i	1.23767	−	1.23767i
$367$	−8.31914	−	3.44590i	−0.434256	−	0.179875i	0.154837	−	0.987940i	$-0.450515\pi$
$367$	−8.31914	−	3.44590i	−0.434256	−	0.179875i	−0.589093	+	0.808065i	$0.700515\pi$
$368$	−3.13228	+	7.56199i	−0.163281	+	0.394196i
$369$	−0.276215	+	0.114412i	−0.0143792	+	0.00595605i
$370$		0			0
$371$	−7.35524	−	17.7571i	−0.381865	−	0.921904i
$372$	0.910649	+	0.910649i	0.0472150	+	0.0472150i
$373$	2.60573			0.134920			0.0674599	−	0.997722i	$-0.478511\pi$
$373$	2.60573			0.134920			0.0674599	+	0.997722i	$0.478511\pi$
$374$	10.1871	−	17.7680i	0.526762	−	0.918761i
$375$		0			0
$376$	−20.1315	−	20.1315i	−1.03820	−	1.03820i
$377$	8.49996	+	20.5207i	0.437770	+	1.05687i
$378$			21.9170i			1.12729i
$379$	−20.1467	+	8.34503i	−1.03487	+	0.428655i	−0.834466	−	0.551059i	$-0.814224\pi$
$379$	−20.1467	+	8.34503i	−1.03487	+	0.428655i	−0.200399	+	0.979714i	$0.564224\pi$
$380$		0			0
$381$	1.82470	+	0.755816i	0.0934823	+	0.0387216i
$382$	7.34614	−	7.34614i	0.375861	−	0.375861i
$383$	−11.8679	+	11.8679i	−0.606423	+	0.606423i	−0.942009	−	0.335587i	$-0.891066\pi$
$383$	−11.8679	+	11.8679i	−0.606423	+	0.606423i	0.335587	+	0.942009i	$0.391066\pi$
$384$	13.4087	+	5.55406i	0.684260	+	0.283430i
$385$		0			0
$386$	−17.5020	+	7.24957i	−0.890829	+	0.368993i
$387$		−	0.376887i		−	0.0191582i
$388$	−1.73574	−	4.19046i	−0.0881191	−	0.212738i
$389$	9.61100	+	9.61100i	0.487297	+	0.487297i	0.907452	−	0.420155i	$-0.138024\pi$
$389$	9.61100	+	9.61100i	0.487297	+	0.487297i	−0.420155	+	0.907452i	$0.638024\pi$
$390$		0			0
$391$	−2.70712	−	9.98271i	−0.136905	−	0.504847i
$392$	15.9264			0.804404
$393$	−13.3644	−	13.3644i	−0.674143	−	0.674143i
$394$	4.66815	+	11.2699i	0.235178	+	0.567769i
$395$		0			0
$396$	−0.425425	+	0.176217i	−0.0213784	+	0.00885523i
$397$	10.5403	−	25.4466i	0.529003	−	1.27713i	−0.403173	−	0.915124i	$-0.632093\pi$
$397$	10.5403	−	25.4466i	0.529003	−	1.27713i	0.932177	−	0.362004i	$-0.117907\pi$
$398$	23.2083	+	9.61320i	1.16333	+	0.481866i
$399$	25.7045	−	25.7045i	1.28684	−	1.28684i
$400$		0			0
$401$	−6.44717	−	2.67050i	−0.321956	−	0.133359i	0.215851	−	0.976426i	$-0.430747\pi$
$401$	−6.44717	−	2.67050i	−0.321956	−	0.133359i	−0.537808	+	0.843068i	$0.680747\pi$
$402$	−14.5478	+	35.1216i	−0.725580	+	1.75171i
$403$	8.12300	−	3.36466i	0.404636	−	0.167606i
$404$		−	5.38332i		−	0.267830i
$405$		0			0
$406$	−17.8995	−	17.8995i	−0.888336	−	0.888336i
$407$	7.39337			0.366476
$408$	−21.9874	+	5.96258i	−1.08854	+	0.295192i
$409$	7.04983			0.348592			0.174296	−	0.984693i	$-0.444235\pi$
$409$	7.04983			0.348592			0.174296	+	0.984693i	$0.444235\pi$
$410$		0			0
$411$	−10.1869	−	24.5933i	−0.502481	−	1.21310i
$412$			1.03900i			0.0511879i
$413$	9.74068	−	4.03472i	0.479307	−	0.198536i
$414$	0.470641	−	1.13623i	0.0231308	−	0.0558426i
$415$		0			0
$416$	−5.02572	+	5.02572i	−0.246406	+	0.246406i
$417$	7.66276	−	7.66276i	0.375247	−	0.375247i
$418$	25.8837	+	10.7214i	1.26602	+	0.524401i
$419$	9.78839	−	23.6313i	0.478194	−	1.15446i	−0.482261	−	0.876028i	$-0.660184\pi$
$419$	9.78839	−	23.6313i	0.478194	−	1.15446i	0.960455	−	0.278435i	$-0.0898158\pi$
$420$		0			0
$421$		−	30.3287i		−	1.47813i	−0.673633	−	0.739066i	$-0.735267\pi$
$421$		−	30.3287i		−	1.47813i	0.673633	−	0.739066i	$-0.264733\pi$
$422$	−9.14299	−	22.0731i	−0.445074	−	1.07450i
$423$	2.53138	+	2.53138i	0.123080	+	0.123080i
$424$	−16.4768			−0.800186
$425$		0			0
$426$	13.0414			0.631859
$427$	−34.8352	−	34.8352i	−1.68580	−	1.68580i
$428$	0.578612	+	1.39689i	0.0279682	+	0.0675213i
$429$			28.0928i			1.35633i
$430$		0			0
$431$	−10.9688	+	26.4811i	−0.528349	+	1.27555i	0.404255	+	0.914646i	$0.367531\pi$
$431$	−10.9688	+	26.4811i	−0.528349	+	1.27555i	−0.932604	+	0.360901i	$0.882469\pi$
$432$	14.5266	+	6.01712i	0.698912	+	0.289499i
$433$	−10.9231	+	10.9231i	−0.524932	+	0.524932i	−0.919057	−	0.394125i	$-0.871048\pi$
$433$	−10.9231	+	10.9231i	−0.524932	+	0.524932i	0.394125	+	0.919057i	$0.371048\pi$
$434$	−7.08540	+	7.08540i	−0.340110	+	0.340110i
$435$		0			0
$436$	−2.00824	+	4.84833i	−0.0961774	+	0.232193i
$437$	13.0716	−	5.41445i	0.625301	−	0.259008i
$438$			15.6552i			0.748033i
$439$	0.616136	+	1.48748i	0.0294066	+	0.0709938i	0.937901	−	0.346904i	$-0.112767\pi$
$439$	0.616136	+	1.48748i	0.0294066	+	0.0709938i	−0.908494	+	0.417898i	$0.862767\pi$
$440$		0			0
$441$	−2.00262			−0.0953627
$442$	−2.72155	+	21.1648i	−0.129451	+	1.00671i
$443$	4.14307			0.196843			0.0984216	−	0.995145i	$-0.468621\pi$
$443$	4.14307			0.196843			0.0984216	+	0.995145i	$0.468621\pi$
$444$	−0.797835	−	0.797835i	−0.0378636	−	0.0378636i
$445$		0			0
$446$			17.0784i			0.808684i
$447$	−25.2158	+	10.4447i	−1.19267	+	0.494018i
$448$	11.8571	−	28.6255i	0.560194	−	1.35243i
$449$	12.2603	+	5.07837i	0.578598	+	0.239663i	0.652737	−	0.757585i	$-0.273621\pi$
$449$	12.2603	+	5.07837i	0.578598	+	0.239663i	−0.0741390	+	0.997248i	$0.523621\pi$
$450$		0			0
$451$	−2.14205	+	2.14205i	−0.100865	+	0.100865i
$452$	3.27544	+	1.35673i	0.154064	+	0.0638153i
$453$	11.1652	−	26.9552i	0.524587	−	1.26647i
$454$	21.8113	−	9.03456i	1.02366	−	0.424013i
$455$		0			0
$456$	−11.9256	−	28.7909i	−0.558467	−	1.34826i
$457$	28.5655	+	28.5655i	1.33624	+	1.33624i	0.899675	+	0.436561i	$0.143804\pi$
$457$	28.5655	+	28.5655i	1.33624	+	1.33624i	0.436561	+	0.899675i	$0.356196\pi$
$458$	−18.0514			−0.843486
$459$	−19.1768	+	5.20039i	−0.895097	+	0.242734i
$460$		0			0
$461$	1.63603	+	1.63603i	0.0761974	+	0.0761974i	0.744178	−	0.667981i	$-0.232841\pi$
$461$	1.63603	+	1.63603i	0.0761974	+	0.0761974i	−0.667981	+	0.744178i	$0.732841\pi$
$462$	−12.2522	−	29.5794i	−0.570023	−	1.37616i
$463$			8.03700i			0.373511i	0.982406	+	0.186756i	$0.0597972\pi$
$463$			8.03700i			0.373511i	−0.982406	+	0.186756i	$0.940203\pi$
$464$	−16.7779	+	6.94964i	−0.778895	+	0.322629i
$465$		0			0
$466$	11.3575	+	4.70443i	0.526126	+	0.217929i
$467$	5.43149	−	5.43149i	0.251339	−	0.251339i	−0.570180	−	0.821520i	$-0.693127\pi$
$467$	5.43149	−	5.43149i	0.251339	−	0.251339i	0.821520	+	0.570180i	$0.193127\pi$
$468$	0.339245	−	0.339245i	0.0156816	−	0.0156816i
$469$	51.6711	+	21.4029i	2.38595	+	0.988292i
$470$		0			0
$471$	−23.9155	+	9.90612i	−1.10197	+	0.456450i
$472$		−	9.03837i		−	0.416025i
$473$	−1.46138	−	3.52808i	−0.0671943	−	0.162221i
$474$	−20.0176	−	20.0176i	−0.919438	−	0.919438i
$475$		0			0
$476$	1.20355	+	4.43817i	0.0551646	+	0.203423i
$477$	2.07183			0.0948626
$478$	16.8531	+	16.8531i	0.770843	+	0.770843i
$479$	−10.3536	−	24.9959i	−0.473070	−	1.14209i	−0.962799	−	0.270217i	$-0.912904\pi$
$479$	−10.3536	−	24.9959i	−0.473070	−	1.14209i	0.489729	−	0.871874i	$-0.337096\pi$
$480$		0			0
$481$	−7.11669	+	2.94783i	−0.324493	+	0.134410i
$482$	−9.94081	+	23.9992i	−0.452792	+	1.09314i
$483$	−14.9380	−	6.18751i	−0.679701	−	0.281541i
$484$	−0.825436	+	0.825436i	−0.0375198	+	0.0375198i
$485$		0			0
$486$	−4.68008	−	1.93855i	−0.212293	−	0.0879345i
$487$	3.66492	−	8.84791i	0.166074	−	0.400937i	−0.818831	−	0.574034i	$-0.805378\pi$
$487$	3.66492	−	8.84791i	0.166074	−	0.400937i	0.984905	+	0.173097i	$0.0553776\pi$
$488$	−39.0180	+	16.1618i	−1.76626	+	0.731610i
$489$		−	27.6767i		−	1.25158i
$490$		0			0
$491$	−4.49913	−	4.49913i	−0.203043	−	0.203043i	0.598259	−	0.801302i	$-0.295859\pi$
$491$	−4.49913	−	4.49913i	−0.203043	−	0.203043i	−0.801302	+	0.598259i	$0.795859\pi$
$492$	0.462307			0.0208424
$493$	11.4144	−	19.9087i	0.514081	−	0.896642i
$494$	−29.1899			−1.31331
$495$		0			0
$496$	2.75097	+	6.64144i	0.123522	+	0.298209i
$497$		−	19.1866i		−	0.860637i
$498$	−33.7314	+	13.9720i	−1.51154	+	0.626101i
$499$	−1.77549	+	4.28642i	−0.0794820	+	0.191887i	−0.958625	−	0.284671i	$-0.908116\pi$
$499$	−1.77549	+	4.28642i	−0.0794820	+	0.191887i	0.879143	+	0.476558i	$0.158116\pi$
$500$		0			0
$501$	−14.2651	+	14.2651i	−0.637318	+	0.637318i
$502$	−4.48644	+	4.48644i	−0.200240	+	0.200240i
$503$	14.6734	+	6.07793i	0.654256	+	0.271002i	0.685019	−	0.728525i	$-0.259794\pi$
$503$	14.6734	+	6.07793i	0.654256	+	0.271002i	−0.0307633	+	0.999527i	$0.509794\pi$
$504$	−1.52507	+	3.68184i	−0.0679320	+	0.164002i
$505$		0			0
$506$		−	12.4613i		−	0.553972i
$507$	−2.05744	−	4.96709i	−0.0913739	−	0.220596i
$508$	−0.241661	−	0.241661i	−0.0107220	−	0.0107220i
$509$	23.6196			1.04692			0.523460	−	0.852050i	$-0.324641\pi$
$509$	23.6196			1.04692			0.523460	+	0.852050i	$0.324641\pi$
$510$		0			0
$511$	23.0320			1.01887
$512$	−17.9808	−	17.9808i	−0.794648	−	0.794648i
$513$	−10.4012	−	25.1106i	−0.459223	−	1.10866i
$514$			22.6258i			0.997981i
$515$		0			0
$516$	−0.223022	+	0.538424i	−0.00981801	+	0.0237028i
$517$	33.5120	+	13.8811i	1.47386	+	0.610492i
$518$	6.20763	−	6.20763i	0.272748	−	0.272748i
$519$	3.01406	−	3.01406i	0.132302	−	0.132302i
$520$		0			0
$521$	4.41375	−	10.6557i	0.193370	−	0.466836i	−0.797222	−	0.603686i	$-0.793698\pi$
$521$	4.41375	−	10.6557i	0.193370	−	0.466836i	0.990592	+	0.136850i	$0.0436979\pi$
$522$	2.52097	−	1.04422i	0.110340	−	0.0457043i
$523$		−	9.73913i		−	0.425862i	−0.977067	−	0.212931i	$-0.931699\pi$
$523$		−	9.73913i		−	0.425862i	0.977067	−	0.212931i	$-0.0683010\pi$
$524$	1.25155	+	3.02151i	0.0546743	+	0.131995i
$525$		0			0
$526$	6.21218			0.270864
$527$	−7.88074	−	4.51834i	−0.343290	−	0.196822i
$528$	−22.9689			−0.999594
$529$	11.8135	+	11.8135i	0.513633	+	0.513633i
$530$		0			0
$531$			1.13650i			0.0493200i
$532$	−5.81146	+	2.40719i	−0.251959	+	0.104365i
$533$	1.20783	−	2.91595i	0.0523168	−	0.126304i
$534$	10.8386	+	4.48951i	0.469033	+	0.194280i
$535$		0			0
$536$	33.9026	−	33.9026i	1.46437	−	1.46437i
$537$	−28.4763	−	11.7953i	−1.22884	−	0.509003i
$538$	6.10142	−	14.7301i	0.263051	−	0.635061i
$539$	−18.7467	+	7.76516i	−0.807480	+	0.334469i
$540$		0			0
$541$	−9.54489	−	23.0434i	−0.410367	−	0.990714i	−0.985039	−	0.172330i	$-0.944870\pi$
$541$	−9.54489	−	23.0434i	−0.410367	−	0.990714i	0.574672	−	0.818384i	$-0.305130\pi$
$542$	27.8861	+	27.8861i	1.19781	+	1.19781i
$543$	11.4873			0.492967
$544$	7.28341	+	0.936561i	0.312273	+	0.0401547i
$545$		0			0
$546$	23.5873	+	23.5873i	1.00944	+	1.00944i
$547$	1.15696	+	2.79316i	0.0494682	+	0.119427i	0.946682	−	0.322170i	$-0.104412\pi$
$547$	1.15696	+	2.79316i	0.0494682	+	0.119427i	−0.897214	+	0.441597i	$0.854412\pi$
$548$			4.60625i			0.196769i
$549$	4.90621	−	2.03222i	0.209392	−	0.0867330i
$550$		0			0
$551$	29.0022	+	12.0131i	1.23554	+	0.511776i
$552$	−9.80116	+	9.80116i	−0.417165	+	0.417165i
$553$	−29.4499	+	29.4499i	−1.25234	+	1.25234i
$554$	6.44739	+	2.67060i	0.273923	+	0.113463i
$555$		0			0
$556$	−1.73245	+	0.717605i	−0.0734723	+	0.0304332i
$557$		−	40.4217i		−	1.71272i	−0.516378	−	0.856361i	$-0.672720\pi$
$557$		−	40.4217i		−	1.71272i	0.516378	−	0.856361i	$-0.327280\pi$
$558$	−0.413348	−	0.997911i	−0.0174984	−	0.0422449i
$559$	2.81338	+	2.81338i	0.118993	+	0.118993i
$560$		0			0
$561$	22.9740	−	17.7388i	0.969963	−	0.748933i
$562$	−35.3718			−1.49207
$563$	−20.7834	−	20.7834i	−0.875917	−	0.875917i	0.117192	−	0.993109i	$-0.462611\pi$
$563$	−20.7834	−	20.7834i	−0.875917	−	0.875917i	−0.993109	+	0.117192i	$0.962611\pi$
$564$	−2.11841	−	5.11430i	−0.0892013	−	0.215351i
$565$		0			0
$566$	−30.0497	+	12.4470i	−1.26309	+	0.523187i
$567$	−13.4081	+	32.3700i	−0.563087	+	1.35941i
$568$	−15.1960	−	6.29440i	−0.637611	−	0.264107i
$569$	−32.3319	+	32.3319i	−1.35543	+	1.35543i	−0.475957	+	0.879469i	$0.657898\pi$
$569$	−32.3319	+	32.3319i	−1.35543	+	1.35543i	−0.879469	+	0.475957i	$0.842102\pi$
$570$		0			0
$571$	18.3776	+	7.61225i	0.769079	+	0.318563i	0.732499	−	0.680768i	$-0.238354\pi$
$571$	18.3776	+	7.61225i	0.769079	+	0.318563i	0.0365794	+	0.999331i	$0.488354\pi$
$572$	1.86029	−	4.49114i	0.0777827	−	0.187784i
$573$	13.6023	−	5.63425i	0.568243	−	0.235374i
$574$			3.59702i			0.150137i
$575$		0			0
$576$	2.36167	+	2.36167i	0.0984031	+	0.0984031i
$577$	−9.01917			−0.375473			−0.187737	−	0.982219i	$-0.560115\pi$
$577$	−9.01917			−0.375473			−0.187737	+	0.982219i	$0.560115\pi$
$578$	19.0268	−	11.1386i	0.791412	−	0.463303i
$579$	−26.8469			−1.11572
$580$		0			0
$581$	20.5557	+	49.6258i	0.852794	+	2.05883i
$582$			33.9945i			1.40912i
$583$	19.3947	−	8.03354i	0.803245	−	0.332715i
$584$	7.55591	−	18.2416i	0.312666	−	0.754842i
$585$		0			0
$586$	−3.87177	+	3.87177i	−0.159941	+	0.159941i
$587$	−2.70370	+	2.70370i	−0.111594	+	0.111594i	−0.760699	−	0.649105i	$-0.775144\pi$
$587$	−2.70370	+	2.70370i	−0.111594	+	0.111594i	0.649105	+	0.760699i	$0.275144\pi$
$588$	2.86096	+	1.18505i	0.117984	+	0.0488705i
$589$	4.75532	−	11.4804i	0.195940	−	0.473040i
$590$		0			0
$591$			17.2873i			0.711105i
$592$	−2.41017	−	5.81867i	−0.0990574	−	0.239146i
$593$	15.0168	+	15.0168i	0.616666	+	0.616666i	0.944675	−	0.328009i	$-0.106378\pi$
$593$	15.0168	+	15.0168i	0.616666	+	0.616666i	−0.328009	+	0.944675i	$0.606378\pi$
$594$	−23.9382			−0.982196
$595$		0			0
$596$	4.72284			0.193455
$597$	25.1731	+	25.1731i	1.03026	+	1.03026i
$598$	4.96848	+	11.9950i	0.203176	+	0.490511i
$599$			32.6292i			1.33319i	0.745418	+	0.666597i	$0.232250\pi$
$599$			32.6292i			1.33319i	−0.745418	+	0.666597i	$0.767750\pi$
$600$		0			0
$601$	−2.64718	+	6.39086i	−0.107981	+	0.260688i	−0.968629	−	0.248511i	$-0.920059\pi$
$601$	−2.64718	+	6.39086i	−0.107981	+	0.260688i	0.860648	+	0.509200i	$0.170059\pi$
$602$	−4.18926	−	1.73525i	−0.170741	−	0.0707234i
$603$	−4.26299	+	4.26299i	−0.173602	+	0.173602i
$604$	−3.56992	+	3.56992i	−0.145258	+	0.145258i
$605$		0			0
$606$	−15.4402	+	37.2759i	−0.627215	+	1.51423i
$607$	−13.0452	+	5.40348i	−0.529487	+	0.219321i	−0.631378	−	0.775475i	$-0.717511\pi$
$607$	−13.0452	+	5.40348i	−0.529487	+	0.219321i	0.101892	+	0.994796i	$0.467511\pi$
$608$			10.0451i			0.407381i
$609$	−13.7283	−	33.1431i	−0.556300	−	1.34303i
$610$		0			0
$611$	−37.7925			−1.52892
$612$	−0.491642	−	0.0632194i	−0.0198735	−	0.00255549i
$613$	10.0581			0.406241			0.203121	−	0.979154i	$-0.434892\pi$
$613$	10.0581			0.406241			0.203121	+	0.979154i	$0.434892\pi$
$614$	−10.0112	−	10.0112i	−0.404019	−	0.404019i
$615$		0			0
$616$			40.3797i			1.62694i
$617$	−0.801835	+	0.332131i	−0.0322807	+	0.0133711i	−0.398765	−	0.917053i	$-0.630561\pi$
$617$	−0.801835	+	0.332131i	−0.0322807	+	0.0133711i	0.366485	+	0.930424i	$0.380561\pi$
$618$	2.98001	−	7.19439i	0.119874	−	0.289401i
$619$	−28.8726	−	11.9594i	−1.16049	−	0.480690i	−0.282451	−	0.959282i	$-0.591148\pi$
$619$	−28.8726	−	11.9594i	−1.16049	−	0.480690i	−0.878038	+	0.478591i	$0.841148\pi$
$620$		0			0
$621$	−8.54829	+	8.54829i	−0.343031	+	0.343031i
$622$	17.2283	+	7.13619i	0.690791	+	0.286135i
$623$	6.60498	−	15.9458i	0.264623	−	0.638857i
$624$	22.1094	−	9.15800i	0.885083	−	0.366614i
$625$		0			0
$626$	0.368771	+	0.890292i	0.0147391	+	0.0355832i
$627$	28.0750	+	28.0750i	1.12121	+	1.12121i
$628$	4.47930			0.178743
$629$	6.90444	+	3.95859i	0.275298	+	0.157839i
$630$		0			0
$631$	11.1868	+	11.1868i	0.445339	+	0.445339i	0.893802	−	0.448463i	$-0.148028\pi$
$631$	11.1868	+	11.1868i	0.445339	+	0.445339i	−0.448463	+	0.893802i	$0.648028\pi$
$632$	13.6633	+	32.9861i	0.543497	+	1.31212i
$633$		−	33.8588i		−	1.34577i
$634$	−25.4164	+	10.5278i	−1.00941	+	0.418112i
$635$		0			0
$636$	−2.95984	−	1.22600i	−0.117365	−	0.0486143i
$637$	14.9491	−	14.9491i	0.592306	−	0.592306i
$638$	19.5501	−	19.5501i	0.773998	−	0.773998i
$639$	1.91078	+	0.791470i	0.0755892	+	0.0313101i
$640$		0			0
$641$	−20.6752	+	8.56394i	−0.816621	+	0.338255i	−0.751592	−	0.659628i	$-0.770714\pi$
$641$	−20.6752	+	8.56394i	−0.816621	+	0.338255i	−0.0650286	+	0.997883i	$0.520714\pi$
$642$		−	11.3321i		−	0.447242i
$643$	16.4195	+	39.6403i	0.647524	+	1.56326i	0.816314	+	0.577608i	$0.196014\pi$
$643$	16.4195	+	39.6403i	0.647524	+	1.56326i	−0.168790	+	0.985652i	$0.553986\pi$
$644$	1.97837	+	1.97837i	0.0779586	+	0.0779586i
$645$		0			0
$646$	18.4315	+	23.8712i	0.725179	+	0.939198i
$647$	−4.56326			−0.179400			−0.0897002	−	0.995969i	$-0.528591\pi$
$647$	−4.56326			−0.179400			−0.0897002	+	0.995969i	$0.528591\pi$
$648$	21.2388	+	21.2388i	0.834337	+	0.834337i
$649$	4.40680	+	10.6390i	0.172982	+	0.417615i
$650$		0			0
$651$	−13.1195	+	5.43427i	−0.514194	+	0.212986i
$652$	−1.83274	+	4.42462i	−0.0717755	+	0.173281i
$653$	−10.3587	−	4.29070i	−0.405366	−	0.167908i	0.170678	−	0.985327i	$-0.445404\pi$
$653$	−10.3587	−	4.29070i	−0.405366	−	0.167908i	−0.576044	+	0.817419i	$0.695404\pi$
$654$	27.8115	−	27.8115i	1.08751	−	1.08751i
$655$		0			0
$656$	2.38411	+	0.987530i	0.0930838	+	0.0385566i
$657$	−0.950096	+	2.29374i	−0.0370668	+	0.0894871i
$658$	39.7923	−	16.4825i	1.55127	−	0.642556i
$659$		−	18.6379i		−	0.726030i	−0.931783	−	0.363015i	$-0.881747\pi$
$659$		−	18.6379i		−	0.726030i	0.931783	−	0.363015i	$-0.118253\pi$
$660$		0			0
$661$	12.3685	+	12.3685i	0.481079	+	0.481079i	0.905476	−	0.424397i	$-0.139514\pi$
$661$	12.3685	+	12.3685i	0.481079	+	0.481079i	−0.424397	+	0.905476i	$0.639514\pi$
$662$	34.8090			1.35289
$663$	−15.0416	+	26.2350i	−0.584166	+	1.01888i
$664$	46.0478			1.78700
$665$		0			0
$666$	0.362141	+	0.874286i	0.0140327	+	0.0338779i
$667$		−	13.9626i		−	0.540636i
$668$	3.22516	−	1.33590i	0.124785	−	0.0516877i
$669$	−9.26207	+	22.3606i	−0.358093	+	0.864512i
$670$		0			0
$671$	38.0477	−	38.0477i	1.46882	−	1.46882i
$672$	8.11707	−	8.11707i	0.313123	−	0.313123i
$673$	21.1257	+	8.75056i	0.814337	+	0.337309i	0.750683	−	0.660663i	$-0.229725\pi$
$673$	21.1257	+	8.75056i	0.814337	+	0.337309i	0.0636539	+	0.997972i	$0.479725\pi$
$674$	−2.21407	+	5.34524i	−0.0852828	+	0.205891i
$675$		0			0
$676$			0.930320i			0.0357815i
$677$	2.95389	+	7.13133i	0.113527	+	0.274079i	0.970423	−	0.241411i	$-0.0776100\pi$
$677$	2.95389	+	7.13133i	0.113527	+	0.274079i	−0.856896	+	0.515490i	$0.827610\pi$
$678$	−18.7889	−	18.7889i	−0.721585	−	0.721585i
$679$	50.0129			1.91932
$680$		0			0
$681$	33.4572			1.28208
$682$	−7.73881	−	7.73881i	−0.296334	−	0.296334i
$683$	−7.12127	−	17.1923i	−0.272488	−	0.657844i	0.727101	−	0.686531i	$-0.240867\pi$
$683$	−7.12127	−	17.1923i	−0.272488	−	0.657844i	−0.999588	+	0.0286872i	$0.990867\pi$
$684$		−	0.678058i		−	0.0259262i
$685$		0			0
$686$	2.96273	−	7.15267i	0.113118	−	0.273090i
$687$	−23.6346	−	9.78977i	−0.901716	−	0.373503i
$688$	−2.30025	+	2.30025i	−0.0876960	+	0.0876960i
$689$	−15.4658	+	15.4658i	−0.589200	+	0.589200i
$690$		0			0
$691$	−6.05603	+	14.6206i	−0.230382	+	0.556192i	−0.996222	−	0.0868389i	$-0.972323\pi$
$691$	−6.05603	+	14.6206i	−0.230382	+	0.556192i	0.765840	+	0.643031i	$0.222323\pi$
$692$	−0.681440	+	0.282262i	−0.0259045	+	0.0107300i
$693$		−	5.07742i		−	0.192875i
$694$	2.31635	+	5.59216i	0.0879275	+	0.212276i
$695$		0			0
$696$	−30.7535			−1.16571
$697$	−3.14730	+	0.853489i	−0.119213	+	0.0323282i
$698$	−2.90334			−0.109893
$699$	12.3190	+	12.3190i	0.465947	+	0.465947i
$700$		0			0
$701$		−	9.63001i		−	0.363721i	−0.983324	−	0.181860i	$-0.941788\pi$
$701$		−	9.63001i		−	0.363721i	0.983324	−	0.181860i	$-0.0582119\pi$
$702$	23.0424	−	9.54446i	0.869678	−	0.360232i
$703$	−4.16621	+	10.0581i	−0.157132	+	0.379349i
$704$	31.2653	+	12.9505i	1.17836	+	0.488091i
$705$		0			0
$706$	−0.527880	+	0.527880i	−0.0198670	+	0.0198670i
$707$	54.8405	+	22.7157i	2.06249	+	0.854311i
$708$	0.672525	−	1.62362i	0.0252750	−	0.0610194i
$709$	−31.8812	+	13.2056i	−1.19732	+	0.495947i	−0.890133	−	0.455701i	$-0.849388\pi$
$709$	−31.8812	+	13.2056i	−1.19732	+	0.495947i	−0.307189	+	0.951648i	$0.599388\pi$
$710$		0			0
$711$	−1.71805	−	4.14774i	−0.0644320	−	0.155553i
$712$	−10.4624	−	10.4624i	−0.392097	−	0.392097i
$713$	−5.52703			−0.206989
$714$	4.39558	−	34.1834i	0.164500	−	1.27928i
$715$		0			0
$716$	3.77136	+	3.77136i	0.140942	+	0.140942i
$717$	12.9258	+	31.2056i	0.482723	+	1.16540i
$718$			14.0498i			0.524334i
$719$	−27.1687	+	11.2536i	−1.01322	+	0.419690i	−0.826629	−	0.562748i	$-0.809744\pi$
$719$	−27.1687	+	11.2536i	−1.01322	+	0.419690i	−0.186592	+	0.982438i	$0.559744\pi$
$720$		0			0
$721$	−10.5844	−	4.38421i	−0.394184	−	0.163276i
$722$	−11.7473	+	11.7473i	−0.437191	+	0.437191i
$723$	−26.0309	+	26.0309i	−0.968101	+	0.968101i
$724$	−1.83645	−	0.760681i	−0.0682510	−	0.0282705i
$725$		0			0
$726$	8.08307	−	3.34812i	0.299991	−	0.124260i
$727$		−	2.80546i		−	0.104049i	−0.998646	−	0.0520243i	$-0.983433\pi$
$727$		−	2.80546i		−	0.104049i	0.998646	−	0.0520243i	$-0.0165673\pi$
$728$	−16.0999	−	38.8686i	−0.596702	−	1.44057i
$729$	16.1182	+	16.1182i	0.596969	+	0.596969i
$730$		0			0
$731$	0.524284	−	4.07723i	0.0193913	−	0.150802i
$732$	−8.21162			−0.303510
$733$	−12.6356	−	12.6356i	−0.466706	−	0.466706i	0.434140	−	0.900846i	$-0.357052\pi$
$733$	−12.6356	−	12.6356i	−0.466706	−	0.466706i	−0.900846	+	0.434140i	$0.857052\pi$
$734$	−4.46901	−	10.7891i	−0.164954	−	0.398234i
$735$		0			0
$736$	4.12781	−	1.70979i	0.152153	−	0.0630239i
$737$	−23.3766	+	56.4361i	−0.861088	+	2.07885i
$738$	−0.358225	−	0.148382i	−0.0131864	−	0.00546200i
$739$	−13.0956	+	13.0956i	−0.481729	+	0.481729i	−0.905684	−	0.423954i	$-0.860642\pi$
$739$	−13.0956	+	13.0956i	−0.481729	+	0.481729i	0.423954	+	0.905684i	$0.360642\pi$
$740$		0			0
$741$	−38.2182	−	15.8305i	−1.40398	−	0.581547i
$742$	9.53905	−	23.0293i	0.350190	−	0.845433i
$743$	34.3835	−	14.2421i	1.26141	−	0.522493i	0.351067	−	0.936350i	$-0.385819\pi$
$743$	34.3835	−	14.2421i	1.26141	−	0.522493i	0.910342	+	0.413858i	$0.135819\pi$
$744$			12.1736i			0.446305i
$745$		0			0
$746$	2.38959	+	2.38959i	0.0874891	+	0.0874891i
$747$	−5.79014			−0.211850
$748$	−4.84746	+	1.31454i	−0.177241	+	0.0480644i
$749$	−16.6718			−0.609175
$750$		0			0
$751$	−0.766504	−	1.85050i	−0.0279701	−	0.0675259i	0.909277	−	0.416191i	$-0.136635\pi$
$751$	−0.766504	−	1.85050i	−0.0279701	−	0.0675259i	−0.937247	+	0.348665i	$0.886635\pi$
$752$		−	30.8995i		−	1.12679i
$753$	−8.30720	+	3.44095i	−0.302731	+	0.125395i
$754$	−11.0236	+	26.6134i	−0.401457	+	0.969204i
$755$		0			0
$756$	3.80045	−	3.80045i	0.138221	−	0.138221i
$757$	−3.30539	+	3.30539i	−0.120137	+	0.120137i	−0.764619	−	0.644482i	$-0.777073\pi$
$757$	−3.30539	+	3.30539i	−0.120137	+	0.120137i	0.644482	+	0.764619i	$0.277073\pi$
$758$	−26.1283	−	10.8227i	−0.949024	−	0.393099i
$759$	6.75811	−	16.3155i	0.245304	−	0.592216i
$760$		0			0
$761$		−	29.1158i		−	1.05545i	−0.849416	−	0.527724i	$-0.823045\pi$
$761$		−	29.1158i		−	1.05545i	0.849416	−	0.527724i	$-0.176955\pi$
$762$	0.980222	+	2.36647i	0.0355097	+	0.0857280i
$763$	−40.9164	−	40.9164i	−1.48127	−	1.48127i
$764$	−2.54766			−0.0921713
$765$		0			0
$766$	−21.7670			−0.786473
$767$	−8.48377	−	8.48377i	−0.306331	−	0.306331i
$768$	−5.22562	−	12.6158i	−0.188563	−	0.455232i
$769$		−	38.6226i		−	1.39277i	−0.717670	−	0.696384i	$-0.754791\pi$
$769$		−	38.6226i		−	1.39277i	0.717670	−	0.696384i	$-0.245209\pi$
$770$		0			0
$771$	−12.2706	+	29.6238i	−0.441915	+	1.06688i
$772$	4.29196	+	1.77779i	0.154471	+	0.0639841i
$773$	−0.520502	+	0.520502i	−0.0187212	+	0.0187212i	−0.716405	−	0.697684i	$-0.754214\pi$
$773$	−0.520502	+	0.520502i	−0.0187212	+	0.0187212i	0.697684	+	0.716405i	$0.254214\pi$
$774$	0.345624	−	0.345624i	0.0124232	−	0.0124232i
$775$		0			0
$776$	16.4073	−	39.6108i	0.588989	−	1.42194i
$777$	11.4942	−	4.76105i	0.412352	−	0.170802i
$778$			17.6276i			0.631978i
$779$	−1.70704	−	4.12116i	−0.0611611	−	0.147656i
$780$		0			0
$781$	20.9560			0.749864
$782$	6.67208	−	11.6372i	0.238593	−	0.416146i
$783$	−26.8223			−0.958550
$784$	12.2225	+	12.2225i	0.436519	+	0.436519i
$785$		0			0
$786$		−	24.5116i		−	0.874299i
$787$	−19.9570	+	8.26645i	−0.711390	+	0.294667i	−0.708879	−	0.705330i	$-0.750799\pi$
$787$	−19.9570	+	8.26645i	−0.711390	+	0.294667i	−0.00251012	+	0.999997i	$0.500799\pi$
$788$	1.14476	−	2.76368i	0.0407802	−	0.0984522i
$789$	8.13359	+	3.36904i	0.289563	+	0.119941i
$790$		0			0
$791$	−27.6424	+	27.6424i	−0.982849	+	0.982849i
$792$	−4.02138	−	1.66571i	−0.142894	−	0.0591884i
$793$	−21.4538	+	51.7940i	−0.761846	+	1.83926i
$794$	33.0018	−	13.6698i	1.17119	−	0.485123i
$795$		0			0
$796$	−2.35742	−	5.69131i	−0.0835564	−	0.201723i
$797$	−34.9907	−	34.9907i	−1.23943	−	1.23943i	−0.960232	−	0.279202i	$-0.909930\pi$
$797$	−34.9907	−	34.9907i	−1.23943	−	1.23943i	−0.279202	−	0.960232i	$-0.590070\pi$
$798$	47.1447			1.66890
$799$	23.8636	+	30.9063i	0.844232	+	1.09339i
$800$		0			0
$801$	1.31557	+	1.31557i	0.0464834	+	0.0464834i
$802$	−3.46339	−	8.36136i	−0.122297	−	0.295250i
$803$			25.1560i			0.887734i
$804$	8.61277	−	3.56752i	0.303749	−	0.125817i
$805$		0			0
$806$	10.5348	+	4.36364i	0.371071	+	0.153703i
$807$	15.9771	−	15.9771i	0.562421	−	0.562421i
$808$	35.9822	−	35.9822i	1.26585	−	1.26585i
$809$	−23.8190	−	9.86614i	−0.837430	−	0.346875i	−0.0775903	−	0.996985i	$-0.524723\pi$
$809$	−23.8190	−	9.86614i	−0.837430	−	0.346875i	−0.759840	+	0.650110i	$0.774723\pi$
$810$		0			0
$811$	23.9380	−	9.91543i	0.840576	−	0.348178i	0.0794951	−	0.996835i	$-0.474669\pi$
$811$	23.9380	−	9.91543i	0.840576	−	0.348178i	0.761081	+	0.648657i	$0.224669\pi$
$812$			6.20760i			0.217844i
$813$	21.3877	+	51.6346i	0.750100	+	1.81090i
$814$	6.78010	+	6.78010i	0.237642	+	0.237642i
$815$		0			0
$816$	−21.4500	−	12.2981i	−0.750899	−	0.430520i
$817$	5.62319			0.196730
$818$	6.46505	+	6.46505i	0.226045	+	0.226045i
$819$	2.02443	+	4.88742i	0.0707394	+	0.170780i
$820$		0			0
$821$	−39.6193	+	16.4108i	−1.38272	+	0.572742i	−0.945208	−	0.326470i	$-0.894141\pi$
$821$	−39.6193	+	16.4108i	−1.38272	+	0.572742i	−0.437514	+	0.899212i	$0.644141\pi$
$822$	13.2114	−	31.8952i	0.460801	−	1.11247i
$823$	24.5942	+	10.1872i	0.857299	+	0.355105i	0.767650	−	0.640869i	$-0.221426\pi$
$823$	24.5942	+	10.1872i	0.857299	+	0.355105i	0.0896482	+	0.995973i	$0.471426\pi$
$824$	−6.94469	+	6.94469i	−0.241930	+	0.241930i
$825$		0			0
$826$	12.6327	+	5.23265i	0.439549	+	0.182067i
$827$	−7.62406	+	18.4061i	−0.265114	+	0.640043i	−0.999240	−	0.0389706i	$-0.987592\pi$
$827$	−7.62406	+	18.4061i	−0.265114	+	0.640043i	0.734126	+	0.679013i	$0.237592\pi$
$828$	−0.278634	+	0.115414i	−0.00968320	+	0.00401091i
$829$		−	22.5258i		−	0.782354i	−0.920315	−	0.391177i	$-0.872068\pi$
$829$		−	22.5258i		−	0.782354i	0.920315	−	0.391177i	$-0.127932\pi$
$830$		0			0
$831$	6.99320	+	6.99320i	0.242592	+	0.242592i
$832$	−35.2588			−1.22238
$833$	−21.6647	−	2.78582i	−0.750636	−	0.0965230i
$834$	14.0543			0.486660
$835$		0			0
$836$	−2.62918	−	6.34739i	−0.0909319	−	0.219529i
$837$			10.6174i			0.366992i
$838$	30.6475	−	12.6946i	1.05870	−	0.438528i
$839$	−1.97898	+	4.77769i	−0.0683221	+	0.164944i	−0.954352	−	0.298684i	$-0.903453\pi$
$839$	−1.97898	+	4.77769i	−0.0683221	+	0.164944i	0.886030	+	0.463628i	$0.153453\pi$
$840$		0			0
$841$	1.39947	−	1.39947i	0.0482575	−	0.0482575i
$842$	27.8130	−	27.8130i	0.958498	−	0.958498i
$843$	−46.3121	−	19.1831i	−1.59507	−	0.660701i
$844$	−2.24211	+	5.41293i	−0.0771766	+	0.186321i
$845$		0			0
$846$			4.64281i			0.159623i
$847$	−4.92576	−	11.8918i	−0.169251	−	0.408609i
$848$	−12.6450	−	12.6450i	−0.434230	−	0.434230i
$849$	−46.0944			−1.58196
$850$		0			0
$851$	4.84232			0.165993
$852$	−2.26140	−	2.26140i	−0.0774744	−	0.0774744i
$853$	−10.9667	−	26.4759i	−0.375492	−	0.906517i	−0.992799	−	0.119795i	$-0.961776\pi$
$853$	−10.9667	−	26.4759i	−0.375492	−	0.906517i	0.617307	−	0.786722i	$-0.288224\pi$
$854$		−	63.8913i		−	2.18632i
$855$		0			0
$856$	−5.46939	+	13.2043i	−0.186940	+	0.451313i
$857$	−21.7270	−	8.99962i	−0.742180	−	0.307421i	−0.0206339	−	0.999787i	$-0.506568\pi$
$857$	−21.7270	−	8.99962i	−0.742180	−	0.307421i	−0.721547	+	0.692366i	$0.756568\pi$
$858$	−25.7625	+	25.7625i	−0.879518	+	0.879518i
$859$	−4.09308	+	4.09308i	−0.139654	+	0.139654i	−0.773478	−	0.633823i	$-0.781485\pi$
$859$	−4.09308	+	4.09308i	−0.139654	+	0.139654i	0.633823	+	0.773478i	$0.281485\pi$
$860$		0			0
$861$	−1.95077	+	4.70957i	−0.0664820	+	0.160502i
$862$	−34.3434	+	14.2255i	−1.16974	+	0.484523i
$863$		−	28.8850i		−	0.983257i	−0.870805	−	0.491629i	$-0.836402\pi$
$863$		−	28.8850i		−	0.983257i	0.870805	−	0.491629i	$-0.163598\pi$
$864$	−3.28452	−	7.92953i	−0.111742	−	0.269768i
$865$		0			0
$866$	−20.0341			−0.680787
$867$	30.9525	−	4.26489i	1.05120	−	0.144843i
$868$	2.45724			0.0834042
$869$	−32.1658	−	32.1658i	−1.09115	−	1.09115i
$870$		0			0
$871$		−	63.6447i		−	2.15652i
$872$	−45.8294	+	18.9831i	−1.55198	+	0.642850i
$873$	−2.06309	+	4.98074i	−0.0698251	+	0.168573i
$874$	16.9527	+	7.02202i	0.573432	+	0.237524i
$875$		0			0
$876$	2.71463	−	2.71463i	0.0917190	−	0.0917190i
$877$	−29.6290	−	12.2727i	−1.00050	−	0.414421i	−0.178520	−	0.983936i	$-0.557131\pi$
$877$	−29.6290	−	12.2727i	−1.00050	−	0.414421i	−0.821981	+	0.569515i	$0.807131\pi$
$878$	−0.799071	+	1.92913i	−0.0269673	+	0.0651049i
$879$	−7.16906	+	2.96952i	−0.241806	+	0.100159i
$880$		0			0
$881$	−7.40726	−	17.8827i	−0.249557	−	0.602484i	0.748609	−	0.663011i	$-0.230722\pi$
$881$	−7.40726	−	17.8827i	−0.249557	−	0.602484i	−0.998167	+	0.0605271i	$0.980722\pi$
$882$	−1.83650	−	1.83650i	−0.0618382	−	0.0618382i
$883$	51.1636			1.72179			0.860896	−	0.508782i	$-0.169904\pi$
$883$	51.1636			1.72179			0.860896	+	0.508782i	$0.169904\pi$
$884$	4.14193	−	3.19809i	0.139308	−	0.107563i
$885$		0			0
$886$	3.79940	+	3.79940i	0.127643	+	0.127643i
$887$	3.36785	+	8.13070i	0.113081	+	0.273002i	0.970281	−	0.241982i	$-0.0777976\pi$
$887$	3.36785	+	8.13070i	0.113081	+	0.273002i	−0.857199	+	0.514985i	$0.827798\pi$
$888$		−	10.6655i		−	0.357910i
$889$	3.48156	−	1.44211i	0.116768	−	0.0483667i
$890$		0			0
$891$	−35.3552	−	14.6446i	−1.18444	−	0.490612i
$892$	2.96142	−	2.96142i	0.0991556	−	0.0991556i
$893$	−37.7685	+	37.7685i	−1.26387	+	1.26387i
$894$	−32.7025	−	13.5458i	−1.09373	−	0.453040i
$895$		0			0
$896$	25.5840	−	10.5972i	0.854700	−	0.354028i
$897$			18.3995i			0.614342i
$898$	6.58616	+	15.9004i	0.219783	+	0.530603i
$899$	−8.67119	−	8.67119i	−0.289200	−	0.289200i
$900$		0			0
$901$	22.4134	+	2.88211i	0.746700	+	0.0960169i
$902$	−3.92874			−0.130813
$903$	−4.54391	−	4.54391i	−0.151212	−	0.151212i
$904$	12.8247	+	30.9615i	0.426542	+	1.02976i
$905$		0			0
$906$	34.9583	−	14.4802i	1.16141	−	0.481073i
$907$	21.7204	−	52.4377i	0.721215	−	1.74117i	0.0513527	−	0.998681i	$-0.483647\pi$
$907$	21.7204	−	52.4377i	0.721215	−	1.74117i	0.669862	−	0.742486i	$-0.266353\pi$
$908$	−5.34873	−	2.21552i	−0.177504	−	0.0735245i
$909$	−4.52447	+	4.52447i	−0.150067	+	0.150067i
$910$		0			0
$911$	21.1007	+	8.74020i	0.699097	+	0.289576i	0.703785	−	0.710413i	$-0.251492\pi$
$911$	21.1007	+	8.74020i	0.699097	+	0.289576i	−0.00468724	+	0.999989i	$0.501492\pi$
$912$	12.9431	−	31.2475i	0.428590	−	1.03471i
$913$	−54.2023	+	22.4513i	−1.79383	+	0.743030i
$914$			52.3919i			1.73297i
$915$		0			0
$916$	3.13014	+	3.13014i	0.103423	+	0.103423i
$917$	−36.0616			−1.19086
$918$	−22.3551	−	12.8171i	−0.737829	−	0.423027i
$919$	24.8236			0.818854			0.409427	−	0.912343i	$-0.365729\pi$
$919$	24.8236			0.818854			0.409427	+	0.912343i	$0.365729\pi$
$920$		0			0
$921$	−7.67826	−	18.5370i	−0.253007	−	0.610813i
$922$			3.00064i			0.0988208i
$923$	−20.1718	+	8.35541i	−0.663961	+	0.275022i
$924$	−3.00456	+	7.25366i	−0.0988429	+	0.238628i
$925$		0			0
$926$	−7.37034	+	7.37034i	−0.242204	+	0.242204i
$927$	0.873240	−	0.873240i	0.0286810	−	0.0286810i
$928$	9.15844	+	3.79355i	0.300640	+	0.124529i
$929$	6.66319	−	16.0864i	0.218612	−	0.527777i	−0.776084	−	0.630629i	$-0.782797\pi$
$929$	6.66319	−	16.0864i	0.218612	−	0.527777i	0.994697	+	0.102852i	$0.0327969\pi$
$930$		0			0
$931$		−	29.8793i		−	0.979253i
$932$	−1.15365	−	2.78517i	−0.0377892	−	0.0912311i
$933$	18.6868	+	18.6868i	0.611777	+	0.611777i
$934$	9.96190			0.325963
$935$		0			0
$936$	4.53503			0.148232
$937$	16.7098	+	16.7098i	0.545886	+	0.545886i	0.925248	−	0.379362i	$-0.123857\pi$
$937$	16.7098	+	16.7098i	0.545886	+	0.545886i	−0.379362	+	0.925248i	$0.623857\pi$
$938$	27.7575	+	67.0125i	0.906314	+	2.18804i
$939$			1.36565i			0.0445663i
$940$		0			0
$941$	−0.563057	+	1.35934i	−0.0183551	+	0.0443132i	−0.932791	−	0.360417i	$-0.882634\pi$
$941$	−0.563057	+	1.35934i	−0.0183551	+	0.0443132i	0.914436	+	0.404730i	$0.132634\pi$
$942$	−31.0161	−	12.8473i	−1.01056	−	0.418588i
$943$	−1.40295	+	1.40295i	−0.0456862	+	0.0456862i
$944$	6.93640	−	6.93640i	0.225761	−	0.225761i
$945$		0			0
$946$	1.89527	−	4.57559i	0.0616206	−	0.148765i
$947$	−14.3084	+	5.92673i	−0.464960	+	0.192593i	−0.602850	−	0.797855i	$-0.705968\pi$
$947$	−14.3084	+	5.92673i	−0.464960	+	0.192593i	0.137889	+	0.990448i	$0.455968\pi$
$948$			6.94216i			0.225471i
$949$	−10.0300	−	24.2146i	−0.325588	−	0.786038i
$950$		0			0
$951$	−38.9870			−1.26424
$952$	−21.6203	+	37.7093i	−0.700716	+	1.22217i
$953$	45.1662			1.46308			0.731538	−	0.681801i	$-0.238803\pi$
$953$	45.1662			1.46308			0.731538	+	0.681801i	$0.238803\pi$
$954$	1.89997	+	1.89997i	0.0615139	+	0.0615139i
$955$		0			0
$956$		−	5.84472i		−	0.189032i
$957$	36.1995	−	14.9943i	1.17016	−	0.484698i
$958$	13.4277	−	32.4173i	0.433829	−	1.04736i
$959$	−46.9243	−	19.4367i	−1.51527	−	0.627643i
$960$		0			0
$961$	18.4879	−	18.4879i	0.596383	−	0.596383i
$962$	−9.22968	−	3.82306i	−0.297577	−	0.123260i
$963$	0.687733	−	1.66033i	0.0221619	−	0.0535035i
$964$	5.88526	−	2.43776i	0.189552	−	0.0785148i
$965$		0			0
$966$	−8.02461	−	19.3731i	−0.258188	−	0.623320i
$967$	−11.4312	−	11.4312i	−0.367601	−	0.367601i	0.499001	−	0.866602i	$-0.333701\pi$
$967$	−11.4312	−	11.4312i	−0.367601	−	0.367601i	−0.866602	+	0.499001i	$0.833701\pi$
$968$	−11.0344			−0.354660
$969$	11.1863	+	41.2503i	0.359356	+	1.32515i
$970$		0			0
$971$	−35.7840	−	35.7840i	−1.14836	−	1.14836i	−0.986874	−	0.161489i	$-0.948370\pi$
$971$	−35.7840	−	35.7840i	−1.14836	−	1.14836i	−0.161489	−	0.986874i	$-0.551630\pi$
$972$	0.475386	+	1.14768i	0.0152480	+	0.0368119i
$973$		−	20.6767i		−	0.662865i
$974$	11.4749	−	4.75306i	0.367679	−	0.152298i
$975$		0			0
$976$	−42.3472	−	17.5408i	−1.35550	−	0.561467i
$977$	19.9582	−	19.9582i	0.638519	−	0.638519i	−0.311671	−	0.950190i	$-0.600889\pi$
$977$	19.9582	−	19.9582i	0.638519	−	0.638519i	0.950190	+	0.311671i	$0.100889\pi$
$978$	25.3810	−	25.3810i	0.811594	−	0.811594i
$979$	17.4164	+	7.21409i	0.556629	+	0.230563i
$980$		0			0
$981$	5.76268	−	2.38698i	0.183988	−	0.0762104i
$982$		−	8.25186i		−	0.263327i
$983$	−15.4012	−	37.1819i	−0.491223	−	1.18592i	−0.954098	−	0.299495i	$-0.903182\pi$
$983$	−15.4012	−	37.1819i	−0.491223	−	1.18592i	0.462875	−	0.886424i	$-0.346818\pi$
$984$	3.09006	+	3.09006i	0.0985076	+	0.0985076i
$985$		0			0
$986$	28.7249	−	7.78966i	0.914787	−	0.248073i
$987$	61.0389			1.94289
$988$	5.06157	+	5.06157i	0.161030	+	0.161030i
$989$	−0.957137	−	2.31073i	−0.0304352	−	0.0734770i
$990$		0			0
$991$	−6.23009	+	2.58059i	−0.197905	+	0.0819751i	−0.479435	−	0.877577i	$-0.659158\pi$
$991$	−6.23009	+	2.58059i	−0.197905	+	0.0819751i	0.281529	+	0.959553i	$0.409158\pi$
$992$	1.50165	−	3.62531i	0.0476775	−	0.115104i
$993$	45.5752	+	18.8779i	1.44629	+	0.599071i
$994$	17.5951	−	17.5951i	0.558082	−	0.558082i
$995$		0			0
$996$	8.27186	+	3.42632i	0.262104	+	0.108567i
$997$	9.51726	−	22.9767i	0.301415	−	0.727679i	−0.698512	−	0.715598i	$-0.746154\pi$
$997$	9.51726	−	22.9767i	0.301415	−	0.727679i	0.999927	−	0.0120812i	$-0.00384567\pi$
$998$	−5.55908	+	2.30265i	−0.175970	+	0.0728891i
$999$		−	9.30211i		−	0.294306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.d.151.5	yes	24
5.2	odd	4		425.2.n.d.49.2		24
5.3	odd	4		425.2.n.e.49.5		24
5.4	even	2		425.2.m.c.151.2	yes	24
17.5	odd	16		7225.2.a.cb.1.5		24
17.8	even	8	inner	425.2.m.d.76.5	yes	24
17.12	odd	16		7225.2.a.cb.1.6		24
85.8	odd	8		425.2.n.d.399.2		24
85.29	odd	16		7225.2.a.bx.1.19		24
85.39	odd	16		7225.2.a.bx.1.20		24
85.42	odd	8		425.2.n.e.399.5		24
85.59	even	8		425.2.m.c.76.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.m.c.76.2	✓	24	85.59	even	8
425.2.m.c.151.2	yes	24	5.4	even	2
425.2.m.d.76.5	yes	24	17.8	even	8	inner
425.2.m.d.151.5	yes	24	1.1	even	1	trivial
425.2.n.d.49.2		24	5.2	odd	4
425.2.n.d.399.2		24	85.8	odd	8
425.2.n.e.49.5		24	5.3	odd	4
425.2.n.e.399.5		24	85.42	odd	8
7225.2.a.bx.1.19		24	85.29	odd	16
7225.2.a.bx.1.20		24	85.39	odd	16
7225.2.a.cb.1.5		24	17.5	odd	16
7225.2.a.cb.1.6		24	17.12	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.917051 + 0.917051i) q^{2} +(0.703348 + 1.69803i) q^{3} -0.318036i q^{4} +(-0.912176 + 2.20219i) q^{6} +(3.23987 + 1.34200i) q^{7} +(2.12576 - 2.12576i) q^{8} +(-0.267297 + 0.267297i) q^{9} +O(q^{10})\)	\(q+(0.917051 + 0.917051i) q^{2} +(0.703348 + 1.69803i) q^{3} -0.318036i q^{4} +(-0.912176 + 2.20219i) q^{6} +(3.23987 + 1.34200i) q^{7} +(2.12576 - 2.12576i) q^{8} +(-0.267297 + 0.267297i) q^{9} +(-1.46576 + 3.53865i) q^{11} +(0.540036 - 0.223690i) q^{12} -3.99064i q^{13} +(1.74044 + 4.20180i) q^{14} +3.26278 q^{16} +(-3.26350 + 2.51983i) q^{17} -0.490250 q^{18} +(-3.98810 - 3.98810i) q^{19} +6.44530i q^{21} +(-4.58929 + 1.90095i) q^{22} +(-0.960003 + 2.31765i) q^{23} +(5.10475 + 2.11446i) q^{24} +(3.65962 - 3.65962i) q^{26} +(4.45222 + 1.84417i) q^{27} +(0.426804 - 1.03040i) q^{28} +(-5.14221 + 2.12997i) q^{29} +(0.843138 + 2.03551i) q^{31} +(-1.25938 - 1.25938i) q^{32} -7.03968 q^{33} +(-5.30361 - 0.681982i) q^{34} +(0.0850102 + 0.0850102i) q^{36} +(-0.738686 - 1.78335i) q^{37} -7.31458i q^{38} +(6.77624 - 2.80681i) q^{39} +(0.730698 + 0.302665i) q^{41} +(-5.91066 + 5.91066i) q^{42} +(-0.704996 + 0.704996i) q^{43} +(1.12542 + 0.466164i) q^{44} +(-3.00578 + 1.24503i) q^{46} -9.47029i q^{47} +(2.29487 + 5.54031i) q^{48} +(3.74605 + 3.74605i) q^{49} +(-6.57414 - 3.76921i) q^{51} -1.26917 q^{52} +(-3.87552 - 3.87552i) q^{53} +(2.39171 + 5.77410i) q^{54} +(9.73994 - 4.03441i) q^{56} +(3.96690 - 9.57696i) q^{57} +(-6.66896 - 2.76238i) q^{58} +(2.12592 - 2.12592i) q^{59} +(-12.9789 - 5.37602i) q^{61} +(-1.09347 + 2.63987i) q^{62} +(-1.22472 + 0.507296i) q^{63} -8.83539i q^{64} +(-6.45574 - 6.45574i) q^{66} +15.9485 q^{67} +(0.801398 + 1.03791i) q^{68} -4.61067 q^{69} +(-2.09375 - 5.05477i) q^{71} +1.13642i q^{72} +(6.06784 - 2.51338i) q^{73} +(0.958006 - 2.31283i) q^{74} +(-1.26836 + 1.26836i) q^{76} +(-9.49772 + 9.49772i) q^{77} +(8.78814 + 3.64017i) q^{78} +(-4.54493 + 10.9724i) q^{79} +9.99115i q^{81} +(0.392528 + 0.947647i) q^{82} +(10.8309 + 10.8309i) q^{83} +2.04984 q^{84} -1.29303 q^{86} +(-7.23353 - 7.23353i) q^{87} +(4.40646 + 10.6381i) q^{88} -4.92175i q^{89} +(5.35543 - 12.9292i) q^{91} +(0.737098 + 0.305316i) q^{92} +(-2.86335 + 2.86335i) q^{93} +(8.68474 - 8.68474i) q^{94} +(1.25268 - 3.02425i) q^{96} +(13.1760 - 5.45769i) q^{97} +6.87064i q^{98} +(-0.554078 - 1.33766i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} + 12 q^{9}+O(q^{10}) \) 24 * q - 8 * q^6 + 12 * q^9	\( 24 q - 8 q^{6} + 12 q^{9} + 4 q^{11} + 12 q^{12} - 24 q^{14} - 24 q^{16} - 4 q^{17} + 40 q^{18} - 20 q^{19} - 16 q^{22} - 8 q^{23} + 16 q^{24} + 16 q^{26} + 12 q^{27} - 48 q^{28} + 4 q^{29} + 24 q^{31} + 60 q^{32} - 48 q^{33} + 16 q^{34} + 60 q^{36} + 12 q^{37} + 8 q^{39} - 20 q^{41} - 12 q^{42} - 32 q^{43} + 64 q^{44} - 40 q^{46} + 40 q^{48} + 24 q^{49} + 16 q^{51} + 48 q^{52} + 12 q^{53} - 20 q^{54} - 32 q^{56} - 68 q^{57} + 16 q^{58} - 16 q^{59} - 64 q^{61} - 100 q^{62} + 44 q^{63} - 72 q^{66} - 40 q^{67} - 20 q^{68} - 48 q^{69} - 24 q^{71} + 32 q^{74} + 52 q^{76} - 24 q^{77} + 16 q^{78} - 48 q^{79} - 100 q^{82} - 12 q^{83} - 40 q^{84} - 16 q^{86} - 24 q^{87} - 4 q^{88} + 24 q^{91} + 88 q^{92} + 32 q^{93} - 40 q^{94} + 132 q^{96} + 88 q^{97} - 80 q^{99}+O(q^{100}) \) 24 * q - 8 * q^6 + 12 * q^9 + 4 * q^11 + 12 * q^12 - 24 * q^14 - 24 * q^16 - 4 * q^17 + 40 * q^18 - 20 * q^19 - 16 * q^22 - 8 * q^23 + 16 * q^24 + 16 * q^26 + 12 * q^27 - 48 * q^28 + 4 * q^29 + 24 * q^31 + 60 * q^32 - 48 * q^33 + 16 * q^34 + 60 * q^36 + 12 * q^37 + 8 * q^39 - 20 * q^41 - 12 * q^42 - 32 * q^43 + 64 * q^44 - 40 * q^46 + 40 * q^48 + 24 * q^49 + 16 * q^51 + 48 * q^52 + 12 * q^53 - 20 * q^54 - 32 * q^56 - 68 * q^57 + 16 * q^58 - 16 * q^59 - 64 * q^61 - 100 * q^62 + 44 * q^63 - 72 * q^66 - 40 * q^67 - 20 * q^68 - 48 * q^69 - 24 * q^71 + 32 * q^74 + 52 * q^76 - 24 * q^77 + 16 * q^78 - 48 * q^79 - 100 * q^82 - 12 * q^83 - 40 * q^84 - 16 * q^86 - 24 * q^87 - 4 * q^88 + 24 * q^91 + 88 * q^92 + 32 * q^93 - 40 * q^94 + 132 * q^96 + 88 * q^97 - 80 * q^99

Introduction

L-functions

Modular forms

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Database

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